{"id":3680,"date":"2021-07-10T11:55:56","date_gmt":"2021-07-10T11:55:56","guid":{"rendered":"https:\/\/themindpalace.in\/?p=3680"},"modified":"2021-08-26T06:56:44","modified_gmt":"2021-08-26T06:56:44","slug":"introduction-to-data-handling","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2021\/07\/10\/introduction-to-data-handling\/","title":{"rendered":"Introduction to Data Handling"},"content":{"rendered":"\n<p>Data handling means to collect and present the data so that it could be used in further studies and to find some results.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Data<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>Any information collected in the form of numbers, words, measurements, symbols, or in any other form is called data.<\/p><\/blockquote><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Graphical Representation of Data<\/strong><\/h3>\n\n\n\n<p>The grouped data can be represented graphically for its clear picture and it is the easiest way to understand the data.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. Pictograph<\/strong><\/h3>\n\n\n\n<p>When we represent the data through pictures or symbols then it is called&nbsp;<strong>Pictograph<\/strong>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"253\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-53.png\" alt=\"\" class=\"wp-image-3681\"\/><\/figure><\/div>\n\n\n\n<p>Here one tree represents 10 trees. And we can easily read the pictograph.<\/p>\n\n\n\n<p>The graph shows that there are 30 trees of apple and so on.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Bar Graphs<\/strong><\/h3>\n\n\n\n<p>In the bar graph, the information represented by the bars of the same width with equal gaps but the height of the bars represents the respective values.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"235\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-55.png\" alt=\"\" class=\"wp-image-3683\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-55.png 479w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-55-300x147.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/figure><\/div>\n\n\n\n<p>Here, the names of pets are represented on the horizontal line and the values of the respective pets are shown by the height of the bars. There is an equal gap between each bar.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3. Double Bar Graph<\/strong><\/h3>\n\n\n\n<p>To compare some data, we can use the double bar graph as it shows the information of two quantities simultaneously.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"522\" height=\"307\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-56.png\" alt=\"\" class=\"wp-image-3684\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-56.png 522w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-56-300x176.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/figure><\/div>\n\n\n\n<p>Here, in the above graph, it represents the marks of the students in two different tests altogether. So we can compare the marks easily.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"591\" height=\"156\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-57.png\" alt=\"\" class=\"wp-image-3685\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-57.png 591w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-57-300x79.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"508\" height=\"272\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-58.png\" alt=\"\" class=\"wp-image-3686\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-58.png 508w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-58-300x161.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"119\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-59.png\" alt=\"\" class=\"wp-image-3687\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-59.png 601w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-59-300x59.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"248\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-61.png\" alt=\"\" class=\"wp-image-3689\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-61.png 507w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-61-300x147.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"516\" height=\"381\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-63.png\" alt=\"\" class=\"wp-image-3691\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-63.png 516w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-63-300x222.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"576\" height=\"336\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-64.png\" alt=\"\" class=\"wp-image-3692\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-64.png 576w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-64-300x175.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Organizing Data<\/strong><\/h2>\n\n\n\n<p>Any data which is available in the unorganized form is called&nbsp;<strong>Raw Data<\/strong>.<\/p>\n\n\n\n<p>This raw data is arranged or grouped in a systematic manner to make it meaningful which is called the&nbsp;<strong>Presentation of Data<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Terms Related to Data Organizing<\/strong><\/h3>\n\n\n\n<p><strong>1. Frequency<\/strong><\/p>\n\n\n\n<p>Frequency tells us the no. of times a particular quantity repeats itself.<\/p>\n\n\n\n<p><strong>2. Frequency Distribution Table<\/strong><\/p>\n\n\n\n<p>Frequency can be represented by the frequency distribution table.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"583\" height=\"223\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-65.png\" alt=\"\" class=\"wp-image-3693\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-65.png 583w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-65-300x115.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/figure><\/div>\n\n\n\n<p>The above table shows the no. of times a particular colour repeat in the bag of skittles.<\/p>\n\n\n\n<p>Frequency can also be shown by the tally marks. A cut over four lines represents the number 5.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"169\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-67.png\" alt=\"\" class=\"wp-image-3695\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-67.png 602w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-67-300x84.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"608\" height=\"228\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-69.png\" alt=\"\" class=\"wp-image-3697\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-69.png 608w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-69-300x113.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/figure><\/div>\n\n\n\n<p><strong>1. Grouping Data<\/strong><\/p>\n\n\n\n<p>If we have a large number of quantities, then we need to group the observation and then make the table. Such a table is called a&nbsp;<strong>Grouped Frequency Distribution Table<\/strong>.<\/p>\n\n\n\n<p><strong>Some Important terms related to grouped Frequency Distribution Table<\/strong><\/p>\n\n\n\n<ul><li><strong>Class Interval or Class:<\/strong>&nbsp;When all the observations are classified in several groups according to their size then these groups are called&nbsp;<strong>Class Interval<\/strong><\/li><\/ul>\n\n\n\n<ul><li><strong>Lower-class Limit:<\/strong>&nbsp;The lowest number in every class interval is known as its&nbsp;<strong>Lower-class Limit<\/strong>.<\/li><\/ul>\n\n\n\n<ul><li><strong>Upper-class Limit:<\/strong>&nbsp;The highest number in every class interval is known as its&nbsp;<strong>Upper-class Limit<\/strong>.&nbsp;<br><\/li><li><strong>Width or Size or Magnitude of the Class Interval:<\/strong>&nbsp;The difference between the upper-class limit and the lower class limit is called the&nbsp;<strong>Size of the Class Interval<\/strong>.&nbsp;<\/li><\/ul>\n\n\n\n<p><strong>Example<\/strong><br>There is a list of marks of 40 students in a school. Arrange this in grouped frequency distribution table.<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"535\" height=\"107\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-71.png\" alt=\"\" class=\"wp-image-3699\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-71.png 535w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-71-300x60.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Solution<\/strong><br>As we can see that the lowest number in the above data is 27 and the highest number is 78, so we can make intervals if 20 &#8211; 30, 30 &#8211; 40 so on.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"272\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-73.png\" alt=\"\" class=\"wp-image-3701\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-73.png 343w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-73-300x238.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Remark:<\/strong>&nbsp;As number 30 comes in two class interval but we cannot count it in both the intervals. So it is to remember that the common observation will always be counted in the higher class. Hence 30 will come in 30-40, not in 20-30.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Histogram<\/strong><\/h2>\n\n\n\n<p>Basically, the bar graph of the grouped frequency distribution or continuous class interval is called&nbsp;<strong>Histogram<\/strong>.<\/p>\n\n\n\n<p>The class intervals are shown on the horizontal line and the frequency of the class interval is shown as the height of the bars.<\/p>\n\n\n\n<p>There is no gap between each bar.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>Draw a histogram for the wages of 30 workers in a company. The wages are as follows: 830, 840, 868, 890, 806, 840, 835, 890,840, 885, 835, 835, 836, 878, 810, 835, 836, 869, 845, 855, 845, 804, 808, 860, 832, 833, 812, 898, 890, 820.<\/p>\n\n\n\n<p><strong>Solution<\/strong><br>Make the grouped frequency distribution of the given data.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-regular\"><table class=\"has-subtle-pale-pink-background-color has-background\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Class Interval<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Frequency<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">800 \u2013 810<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">810 \u2013 820<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">820 \u2013 830<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">830 \u2013 840<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">840 \u2013 850<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">850 \u2013 860<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">860 \u2013 870<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">870 \u2013 880<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">880 \u2013 890<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">890 \u2013 900<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Draw the histogram by taking the class interval on the horizontal line and the frequency on the vertical line.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"271\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-74.png\" alt=\"\" class=\"wp-image-3702\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-74.png 407w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-74-300x200.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Remark:&nbsp;<\/strong>As the class interval does not start from zero, so we will put a jagged line which shows that there is no number between 0 \u2013 800.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Circle Graph or Pie Chart<\/strong><\/h2>\n\n\n\n<p>If we represent the data in a circle form then it is said to be a pie chart. This graph shows the relationship between the whole and its part. We have to divide the circle into sectors and each sector is proportional to its respective activity.<\/p>\n\n\n\n<p>We use it when we have information on percentage or fraction.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Drawing of a Pie Chart<\/strong><\/h3>\n\n\n\n<p>If we have the information in percentage then we need to calculate the respective angles to show them in the pie chart.<\/p>\n\n\n\n<p>As we know that a complete circle is of 360\u00b0, so we need to calculate the fraction of 360\u00b0 for every sector.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>Draw a pie chart of the following percentage of genres of movies liked by the public.<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-regular\"><table class=\"has-subtle-pale-pink-background-color has-background\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Genres of Movie<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Percentage of the no. of people<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Comedy<\/td><td class=\"has-text-align-center\" data-align=\"center\">27%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Action<\/td><td class=\"has-text-align-center\" data-align=\"center\">18%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Romance<\/td><td class=\"has-text-align-center\" data-align=\"center\">14%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Drama<\/td><td class=\"has-text-align-center\" data-align=\"center\">14%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Horror<\/td><td class=\"has-text-align-center\" data-align=\"center\">11%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Foreign<\/td><td class=\"has-text-align-center\" data-align=\"center\">8%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Science fiction<\/td><td class=\"has-text-align-center\" data-align=\"center\">8%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Solution<\/strong><br>To draw the pie chart first we need to calculate the angle by taking the fraction of 360\u00b0.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"761\" height=\"209\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-77.png\" alt=\"\" class=\"wp-image-3706\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-77.png 761w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-77-300x82.png 300w\" sizes=\"(max-width: 761px) 100vw, 761px\" \/><\/figure><\/div>\n\n\n\n<p>By using these angles draw a pie chart.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"295\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-78.png\" alt=\"\" class=\"wp-image-3707\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-78.png 416w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-78-300x213.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_00eee2-e8\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>Exercise 3.1<\/strong><\/p>\n\n\n\n<ol type=\"1\"><li><strong>For which of these would you use a histogram to show the data?<br><\/strong>(i) The number of letters for different areas in a postman\u2019s bag.<br>(ii) The height of competitors in an athletics meet.<br>(iii) The number of cassettes produced by 5 companies.<br>(iv) The number of passengers boarding trains from 7 a.m to 7 p.m at a station.<br>Give a reason for each.<\/li><\/ol>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) The number of areas cannot be represented in class-intervals. So, we cannot use the histogram to show the data.<\/p>\n\n\n\n<p> (ii) Height of competitors can be divided into intervals. So, we can use histogram here.<br>For example:<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"140\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-81.png\" alt=\"\" class=\"wp-image-3710\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-81.png 349w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-81-300x120.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/figure><\/div>\n\n\n\n<p>(iii) Companies cannot be divided into intervals. So, we cannot use histogram here.<\/p>\n\n\n\n<p>(iv) Time for boarding the train can be divided into intervals. So, we can use histogram here.<br>For example:<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"137\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-82.png\" alt=\"\" class=\"wp-image-3711\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-82.png 346w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-82-300x119.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_dba0b9-ee\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p>2. <strong>The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning.<br><\/strong>W W W G B W W M G G M M W W W W<br>G B M W B G G M W W M M W W W<br>M W B W G M W W W W G W M M W<br>W M W G W M G W M M B G G W<br><strong>Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"493\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-83.png\" alt=\"\" class=\"wp-image-3712\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-83.png 384w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-83-234x300.png 234w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/figure><\/div>\n\n\n\n<p><strong>3. The weekly wages (in \u20b9) of 30 workers in a factory are:<br><\/strong>830, 835, 890, 810, 835, 836, 869, 845, 898, 890,<br>820, 860, 832, 833, 855, 845, 804, 808, 812, 840,<br>885, 835, 835, 836, 878, 840, 868, 890, 806, 840<br><strong>Using tally marks make a frequency table with intervals as 800-810, 810-820 and so on.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"154\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-86.png\" alt=\"\" class=\"wp-image-3715\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-86.png 373w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-86-300x124.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"372\" height=\"161\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-87.png\" alt=\"\" class=\"wp-image-3716\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-87.png 372w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-87-300x130.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/figure><\/div>\n\n\n\n<p><strong>4. Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions:<br><\/strong>(i) Which group has the maximum number of workers?<br>(ii) How many workers earn \u20b9 850 and more?<br>(iii) How many workers earn less than \u20b9 850?<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<br>Refer to the frequency table of Question No. 3.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"404\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-88.png\" alt=\"\" class=\"wp-image-3717\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-88.png 355w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-88-264x300.png 264w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/figure><\/div>\n\n\n\n<p>(I) Group 830-840 has the maximum number of workers, i.e., 9.<br>(ii) 10 workers earn equal and more than \u20b9 850.<br>(iii) 20 workers earn less than \u20b9 850.<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_dbb0d5-d9\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>5. The number of hours for which students of a particular class watched television during holidays is shown through the given graph.<br><\/strong>Answer the following questions.<br>(i) For how many hours did the maximum number of students watch TV?<br>(ii) How many students watched TV for less than 4 hours?<br>(iii) How many students spent more than 5 hours watching TV?<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"383\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-89.png\" alt=\"\" class=\"wp-image-3718\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-89.png 333w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-89-261x300.png 261w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) 32 is the maximum number of students who watched TV for 4 to 5 hours.<br>(ii) 4 + 8 + 22 = 34 students watched TV for less than 4 hours.<br>(iii) 8 + 6 = 14 students watched TV for more than 5 hours.<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_299be9-3a\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>Example 2: <\/strong><\/p>\n\n\n\n<p><strong>On a particular day, the sales (in rupees) of different items of a baker\u2019s shop are given below.<\/strong><\/p>\n\n\n\n<p>ordinary bread : 320<br>fruit bread : 80<br>cakes and pastries : 160 <br>biscuits : 120<br>others : 40<br><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">Total : 720<\/span><\/strong><\/p>\n\n\n\n<p><strong>Draw a pie chart for this data.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>: <\/p>\n\n\n\n<p>We find the central angle of each sector. Here the total sale = ` 720. We thus have this table<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"531\" height=\"324\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-91.png\" alt=\"\" class=\"wp-image-3720\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-91.png 531w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-91-300x183.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/figure><\/div>\n\n\n\n<p>Now, we make the pie chart (Fig 5.8):<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"215\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-92.png\" alt=\"\" class=\"wp-image-3721\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">TRY THESE<\/h2>\n\n\n\n<p>Draw a pie chart of the data given below.<br>The time spent by a child during a day.<br>Sleep \u2014 8 hours<br>School \u2014 6 hours<br>Home work \u2014 4 hours<br>Play \u2014 4 hours<br>Others \u2014 2 hours<\/p>\n\n\n\n<p><strong>Total hours spent =24<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"270\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-93.png\" alt=\"\" class=\"wp-image-3723\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-93.png 587w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-93-300x138.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"229\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-94.png\" alt=\"\" class=\"wp-image-3724\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_afb941-69\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>&nbsp;Exercise 5.2<\/strong> <\/h2>\n\n\n\n<ol><li><strong>A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey<\/strong><\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"259\" height=\"222\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-96.png\" alt=\"\" class=\"wp-image-3726\"\/><\/figure><\/div>\n\n\n\n<p>From this pie chart answer the following:<br>(i) If 20 people liked classical music, how many young people were surveyed?<br>(ii) Which type of music is liked by the maximum number of people?<br>(iii) If a cassette company were to make 1000 CDs. How many of each type would they make?<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) Number of young people who were surveyed =&nbsp;100\u00d720\/10&nbsp;= 200 people.<br>(ii) Light music is liked by the maximum people, i.e., 40%<br>(iii) Total number of CD = 1000<br>Number of viewers who like classical music =&nbsp;10\u00d71000\/100&nbsp;= 100<br>Number of viewer who like semi-classical music =&nbsp;20\u00d71000\/100&nbsp;= 200<br>Number of viewers who like light music =&nbsp;40\u00d71000\/100&nbsp;= 400<br>Number of viewers who like folk music =&nbsp;30\u00d71000\/100&nbsp;= 300 <\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_5f4c18-da\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>2. A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.<br><\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"375\" height=\"397\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-98.png\" alt=\"\" class=\"wp-image-3728\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-98.png 375w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-98-283x300.png 283w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/figure><\/div>\n\n\n\n<p>(i) Which season got the most votes?<br>(ii) Find the central angle of each sector.<br>(iii) Draw a pie chart to show this information.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) Winter season got the most votes, i.e. 150<\/p>\n\n\n\n<p>(ii) <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"245\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-99.png\" alt=\"\" class=\"wp-image-3729\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-99.png 343w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-99-300x214.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/figure><\/div>\n\n\n\n<p><br>(iii)Pie chart<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"208\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-100.png\" alt=\"\" class=\"wp-image-3730\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_972bea-86\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"378\" height=\"189\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-102.png\" alt=\"\" class=\"wp-image-3732\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-102.png 378w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-102-300x150.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Solution<\/strong>:<br>Table to find the central angle of each sector<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"375\" height=\"310\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-105.png\" alt=\"\" class=\"wp-image-3735\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-105.png 375w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-105-300x248.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/pie1.png\" alt=\"\" class=\"wp-image-3736\" width=\"283\" height=\"279\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/pie1.png 566w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/pie1-300x296.png 300w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/pie1-80x80.png 80w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_1f5e91-3c\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>4. The following pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"251\" height=\"244\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-106.png\" alt=\"\" class=\"wp-image-3737\"\/><\/figure><\/div>\n\n\n\n<p>i) In which subject did the student score 105 marks?<br>(Hint: for 540 marks, the central angle = 360\u00b0. So, for 105 marks, what is the central angle?)<br>(ii) How many more marks were obtained by the student in Mathematics than in Hindi?<br>(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.<br>(Hint: Just study the central angles). <\/p>\n\n\n\n<p><strong>Solution<\/strong>: <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-107.png\" alt=\"\" class=\"wp-image-3738\" width=\"280\" height=\"159\"\/><\/figure><\/div>\n\n\n\n<p>(I) For 540 marks, the central angle = 360\u00b0<br>For 105 marks the central angle =\u00a0360\/540\u00d7105\u00a0= 70\u00b0<br>Corresponding subject = Hindi<br><br>(ii) Marks obtained in Mathematics =\u00a090\/360\u00d7540\u00a0= 135<br>Marks obtained in Mathematics more than Hindi = 135 \u2013 105 = 30<br><br>(iii) Central angle of Social Science + Mathematics = 65\u00b0 + 90\u00b0 = 155\u00b0<br>Central angle of Science + Hindi = 80\u00b0 + 70\u00b0 = 150\u00b0<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_b678c3-c9\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p>5<strong>. Marks obtained in Social Science and Mathematics are more than that of the marks obtained in Science and Hindi.<\/strong><br>The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.<br><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Language<\/th><th class=\"has-text-align-center\" data-align=\"center\">Number <br>of students<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Hindi<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>40 <\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">English<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>12 <\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Marathi<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>9 <\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Tamil<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>7 <\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Bengali<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4 <\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">Total<\/span><\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">72<\/span><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"376\" height=\"334\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-108.png\" alt=\"\" class=\"wp-image-3741\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-108.png 376w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-108-300x266.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"264\" height=\"226\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-109.png\" alt=\"\" class=\"wp-image-3742\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Chance and Probability<\/strong><\/h2>\n\n\n\n<p>Probability tells the degree of uncertainty. It&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Measure_(mathematics)\"><strong>measures<\/strong><\/a>&nbsp;the likelihood that an&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Event_(probability_theory)\"><strong>event<\/strong><\/a>&nbsp;will occur.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Random Experiment<\/strong><\/h3>\n\n\n\n<p>If the result of the experiment is not known then it is known as a random experiment.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>If we throw a dice, then the result could be any number from 1 \u2013 6.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"127\" height=\"86\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-110.png\" alt=\"\" class=\"wp-image-3743\"\/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Outcomes<\/strong><\/h3>\n\n\n\n<p>When we do an experiment then there could be different results, these possible results of the random experiment are called outcomes.<\/p>\n\n\n\n<p><strong>Example<\/strong><\/p>\n\n\n\n<p>There are two possible outcomes when we toss a coin i.e. head and tail.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Equally Likely Outcomes<\/strong><\/h3>\n\n\n\n<p>If every outcome has the same possibility of occurring these outcomes are called&nbsp;<strong>Equally Likely Outcomes<\/strong>.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>If we throw a dice, then there is an equal chance of every no. to come while doing the random experiment. i.e. a dice has the same possibility of getting 1, 2, 3, 4, 5 and 6.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Linking Chances to the Probability<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"65\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-111.png\" alt=\"\" class=\"wp-image-3744\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-111.png 459w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-111-300x42.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Example<\/strong><br>What is the chance of getting 3 when we throw a dice?<\/p>\n\n\n\n<p><strong>Solution<\/strong><br>There is only one chance to get 3 in one throw and the total possible outcomes are 6.<\/p>\n\n\n\n<p>Hence the probability of getting =1\/6.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Outcomes as Events<\/strong><\/h3>\n\n\n\n<p>Each outcome or collection of outcomes of an experiment is known as an event.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"339\" height=\"61\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-112.png\" alt=\"\" class=\"wp-image-3745\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-112.png 339w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-112-300x54.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Example<\/strong><br>If we throw a dice then getting each outcome 1, 2, 3, 4, 5, and 6 are events.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>What is the event of getting odd numbers when we throw a dice?<\/p>\n\n\n\n<p><strong>Solution<\/strong><br>The probability of getting an odd number is 3(odd numbers are 1, 3, 5)<\/p>\n\n\n\n<p>The total number of outcomes is 6.<\/p>\n\n\n\n<p>The probability of getting an odd number = 3\/6.<\/p>\n\n\n\n<p><strong>Example<\/strong><br>What is the probability of spinning yellow?<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"143\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-113.png\" alt=\"\" class=\"wp-image-3746\"\/><\/figure><\/div>\n\n\n\n<p>Here number of chances to come yellow while spinning is 3.<\/p>\n\n\n\n<p>The total number of outcomes is 8.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"530\" height=\"108\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-115.png\" alt=\"\" class=\"wp-image-3748\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-115.png 530w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-115-300x61.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_a3c939-ba\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Exercise 3.3 <\/h3>\n\n\n\n<ol><li><strong>List the outcomes you can see in these experiments.<br><\/strong>(i) Spinning a wheel<br>(ii) Tossing two coins together<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"171\" height=\"167\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-116.png\" alt=\"\" class=\"wp-image-3749\"\/><\/figure><\/div>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>(i) On spinning the wheel, we can get the following outcomes B, C, D, E and A.<br><br>(ii) When two coins are tossed together, we get the following outcomes<br>HH, HT, TH, TT (Where H denotes Head and T denotes Tail)<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_169dee-fe\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>2. When a die is thrown, list the outcomes of an event of getting<br><\/strong>(i) (a) a prime number<br>(b) not a prime number<br>(ii) (a) a number greater than 5<br>(b) a number not greater than 5<\/p>\n\n\n\n<p>Solution:<br>(i) (a) The prime number are 2, 3 and 5<br>Required outcomes = 2, 3 and 5<br>(b) Outcomes for not a prime number are 1, 4 and 6<br>Required outcomes = 1, 4, 6.<br><br>(ii) (a) Outcomes for a number greater than 5 = 6<br>Required outcome = 6<br>(b) Outcomes for a number not greater than 5 are 1, 2, 3, 4, 5<br>Required outcomes = 1, 2, 3, 4, 5.<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_061807-21\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>3. Find the<br><\/strong>(i) Probability of the pointer stopping on D in (Question 1-(a))?<br>(ii) Probability of getting an ace from a well-shuffled deck of 52 playing cards?<br>(iii) Probability of getting a red apple, (see figure below)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"174\" height=\"173\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-117.png\" alt=\"\" class=\"wp-image-3750\" srcset=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-117.png 174w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-117-150x150.png 150w, https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-117-80x80.png 80w\" sizes=\"(max-width: 174px) 100vw, 174px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) Refer to fig. Question 1-(a)<br>Total number of sectors = 5<br>Number of sector where the pointer stops = 1, i.e. D<br>Probability of pointer stopping at D =\u00a015<br><br>(ii)\u00a0 Number of aces = 4 (one from each suit i.e. heart, diamond, club and spade)<br>Total number of playing cards = 52<br>Probability of getting an ace<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"271\" height=\"95\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-118.png\" alt=\"\" class=\"wp-image-3751\"\/><\/figure><\/div>\n\n\n\n<p><br><\/p>\n\n\n\n<p>(iii) Total number of apples = 7<br>Number of red apples = 4<br>Probability of getting red apples<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"58\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-120.png\" alt=\"\" class=\"wp-image-3753\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_badd6c-a1\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box, and mixed well. One slip is chosen from the box without looking into it. What is the probability of:<br><\/strong>(i) getting a number 6?<br>(ii) getting a number less than 6?<br>(iii) getting a number greater than 6?<br>(iv) getting a 1-digit number?<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<br>(i) Probability of getting a number 6 =\u00a0110<br><br>(ii) Probability of getting a number less than 6 =\u00a0510\u00a0=\u00a012\u00a0[\u2235 Numbers less than 6 are 1, 2, 3, 4, 5]<br><br>(iii) Probability of getting a number greater than 6 =\u00a0410\u00a0=\u00a025\u00a0[\u2235 Number greater than 6 are 7, 8, 9, 10]<br><br>(iv) Probability of getting a 1-digit number =\u00a0910<br>[\u2235 1-digit numbers are 9, i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9]<\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_fdb56f-a6\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector? <\/strong><br><br><strong>Solution:<br><\/strong>Total number of sectors are = 3 green + 1 blue + 1 red = 5 sectors<br>Probability of getting a green sector<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"270\" height=\"53\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-121.png\" alt=\"\" class=\"wp-image-3754\"\/><\/figure><\/div>\n\n\n\n<p>Number of non-blue sectors are = 3 green + 1 red = 4 sectors<br>Probability of getting non-blue sector<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"56\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-123.png\" alt=\"\" class=\"wp-image-3756\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_2b1aa1-88\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><strong>6. Find the probabilities of the events given in Question 2.<br><\/strong><br><strong>Solution:<br><\/strong>Refer to Question 2, we have<br>(i) (a) Probability of getting a prime number<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"101\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-124.png\" alt=\"\" class=\"wp-image-3757\"\/><\/figure><\/div>\n\n\n\n<p>(b) Probability of getting a non-prime number<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"92\" src=\"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-125.png\" alt=\"\" class=\"wp-image-3758\"\/><\/figure><\/div>\n\n\n\n<p>(ii) (a) Probability of getting a number greater than 5 =\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"8\" height=\"33\" src=\"\">1\/6<br>(b) Probability of a number not greater than 5 =\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"34\" src=\"\">or, 1 \u2013\u00a01\/6= 5\/6\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"34\" src=\"\"><\/p>\n\n\n\n<div class=\"wp-block-kadence-spacer aligncenter kt-block-spacer-_9e7749-2f\"><div class=\"kt-block-spacer kt-block-spacer-halign-center\" style=\"height:60px\"><hr class=\"kt-divider\" style=\"border-top-color:rgba(238, 238, 238, 1);border-top-width:1px;width:80%;border-top-style:solid\"\/><\/div><\/div>\n\n\n\n<p><br><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Data handling means to collect and present the data so that it could be used in further studies and to find some results. Data Any information collected in the form of numbers, words, measurements,&#46;&#46;&#46;<\/p>\n","protected":false},"author":2,"featured_media":3684,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[110,475,14],"tags":[],"cp_meta_data":{"_jetpack_related_posts_cache":["a:1:{s:32:\"8f6677c9d6b0f903e98ad32ec61f8deb\";a:2:{s:7:\"expires\";i:1776617865;s:7:\"payload\";a:3:{i:0;a:1:{s:2:\"id\";i:2321;}i:1;a:1:{s:2:\"id\";i:2251;}i:2;a:1:{s:2:\"id\";i:6317;}}}}"],"_edit_lock":["1629961004:2"],"_last_editor_used_jetpack":["block-editor"],"_edit_last":["2"],"_layout":["inherit"],"_heateor_sss_meta":["a:2:{s:7:\"sharing\";i:0;s:16:\"vertical_sharing\";i:0;}"],"_thumbnail_id":["3684"]},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/themindpalace.in\/wp-content\/uploads\/2021\/07\/image-56.png","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/3680"}],"collection":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/comments?post=3680"}],"version-history":[{"count":9,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/3680\/revisions"}],"predecessor-version":[{"id":3763,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/3680\/revisions\/3763"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media\/3684"}],"wp:attachment":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media?parent=3680"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/categories?post=3680"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/tags?post=3680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}