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Page 1 30. Find the median of the following data b Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of Students 5 3 4 3 3 4 7 9 7 8 Sol: The frequency distribution table of less than type is given as follows: Marks (upper class limits) Cumulative frequency (cf) Less than 10 5 Less than 20 5 + 3 = 8 Less than 30 8 + 4 = 12 Less than 40 12 + 3 = 15 Less than 50 15 + 3 = 18 Less than 60 18 + 4 = 22 Less than 70 22 + 7 = 29 Less than 80 29 + 9 = 38 Less than 90 38 + 7 = 45 Less than 100 45 + 8 = 53 Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 53 = 26.5. Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4. Page 2 30. Find the median of the following data b Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of Students 5 3 4 3 3 4 7 9 7 8 Sol: The frequency distribution table of less than type is given as follows: Marks (upper class limits) Cumulative frequency (cf) Less than 10 5 Less than 20 5 + 3 = 8 Less than 30 8 + 4 = 12 Less than 40 12 + 3 = 15 Less than 50 15 + 3 = 18 Less than 60 18 + 4 = 22 Less than 70 22 + 7 = 29 Less than 80 29 + 9 = 38 Less than 90 38 + 7 = 45 Less than 100 45 + 8 = 53 Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 53 = 26.5. Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4. Thus, median of the data is 66.4. 31. The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of Wickets Less than 15 Less than 30 Less than 45 Less than 60 Less than 75 Less than 90 Less than 105 Less than 120 Number of bowlers 2 5 9 17 39 54 70 80 Sol: Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Page 3 30. Find the median of the following data b Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of Students 5 3 4 3 3 4 7 9 7 8 Sol: The frequency distribution table of less than type is given as follows: Marks (upper class limits) Cumulative frequency (cf) Less than 10 5 Less than 20 5 + 3 = 8 Less than 30 8 + 4 = 12 Less than 40 12 + 3 = 15 Less than 50 15 + 3 = 18 Less than 60 18 + 4 = 22 Less than 70 22 + 7 = 29 Less than 80 29 + 9 = 38 Less than 90 38 + 7 = 45 Less than 100 45 + 8 = 53 Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 53 = 26.5. Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4. Thus, median of the data is 66.4. 31. The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of Wickets Less than 15 Less than 30 Less than 45 Less than 60 Less than 75 Less than 90 Less than 105 Less than 120 Number of bowlers 2 5 9 17 39 54 70 80 Sol: Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 80 = 40. Mark the point A whose ordinate is 40 and its x-coordinate is 76. Thus, median of the data is 76. 32. Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80 No of Students 4 6 10 10 25 22 18 5 Sol: The frequency distribution table of more than type is as follows: Marks (upper class limits) Cumulative frequency (cf) More than 0 96 + 4 = 100 More than 10 90 + 6 = 96 More than 20 80 + 10 = 90 More than 30 70 + 10 = 80 More than 40 45 + 25 = 70 More than 50 23 + 22 = 45 More than 60 18 + 5 = 23 More than 70 5 Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: Page 4 30. Find the median of the following data b Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of Students 5 3 4 3 3 4 7 9 7 8 Sol: The frequency distribution table of less than type is given as follows: Marks (upper class limits) Cumulative frequency (cf) Less than 10 5 Less than 20 5 + 3 = 8 Less than 30 8 + 4 = 12 Less than 40 12 + 3 = 15 Less than 50 15 + 3 = 18 Less than 60 18 + 4 = 22 Less than 70 22 + 7 = 29 Less than 80 29 + 9 = 38 Less than 90 38 + 7 = 45 Less than 100 45 + 8 = 53 Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 53 = 26.5. Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4. Thus, median of the data is 66.4. 31. The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of Wickets Less than 15 Less than 30 Less than 45 Less than 60 Less than 75 Less than 90 Less than 105 Less than 120 Number of bowlers 2 5 9 17 39 54 70 80 Sol: Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 80 = 40. Mark the point A whose ordinate is 40 and its x-coordinate is 76. Thus, median of the data is 76. 32. Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80 No of Students 4 6 10 10 25 22 18 5 Sol: The frequency distribution table of more than type is as follows: Marks (upper class limits) Cumulative frequency (cf) More than 0 96 + 4 = 100 More than 10 90 + 6 = 96 More than 20 80 + 10 = 90 More than 30 70 + 10 = 80 More than 40 45 + 25 = 70 More than 50 23 + 22 = 45 More than 60 18 + 5 = 23 More than 70 5 Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: 33. The heights of 50 girls of Class X of a school are recorded as follows: Height (in cm) 135 - 140 140 145 145 150 150 155 155 160 160 165 No of Students 5 8 9 12 14 2 for the above data. Sol: The frequency distribution table of more than type is as follows: Height (in cm) (lower class limit) Cumulative frequency (cf) More than 135 5 + 45 = 50 More than 140 8 + 37 = 45 More than 145 9 + 28 = 37 More than 150 12 + 16 = 28 More than 155 14 + 2 = 16 More than 160 2 Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: Page 5 30. Find the median of the following data b Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of Students 5 3 4 3 3 4 7 9 7 8 Sol: The frequency distribution table of less than type is given as follows: Marks (upper class limits) Cumulative frequency (cf) Less than 10 5 Less than 20 5 + 3 = 8 Less than 30 8 + 4 = 12 Less than 40 12 + 3 = 15 Less than 50 15 + 3 = 18 Less than 60 18 + 4 = 22 Less than 70 22 + 7 = 29 Less than 80 29 + 9 = 38 Less than 90 38 + 7 = 45 Less than 100 45 + 8 = 53 Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 53 = 26.5. Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4. Thus, median of the data is 66.4. 31. The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of Wickets Less than 15 Less than 30 Less than 45 Less than 60 Less than 75 Less than 90 Less than 105 Less than 120 Number of bowlers 2 5 9 17 39 54 70 80 Sol: Taking upper class limits of class intervals on x-axis and their respective frequencies on y- axis, its ogive can be drawn as follows: Here, N = 80 = 40. Mark the point A whose ordinate is 40 and its x-coordinate is 76. Thus, median of the data is 76. 32. Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80 No of Students 4 6 10 10 25 22 18 5 Sol: The frequency distribution table of more than type is as follows: Marks (upper class limits) Cumulative frequency (cf) More than 0 96 + 4 = 100 More than 10 90 + 6 = 96 More than 20 80 + 10 = 90 More than 30 70 + 10 = 80 More than 40 45 + 25 = 70 More than 50 23 + 22 = 45 More than 60 18 + 5 = 23 More than 70 5 Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: 33. The heights of 50 girls of Class X of a school are recorded as follows: Height (in cm) 135 - 140 140 145 145 150 150 155 155 160 160 165 No of Students 5 8 9 12 14 2 for the above data. Sol: The frequency distribution table of more than type is as follows: Height (in cm) (lower class limit) Cumulative frequency (cf) More than 135 5 + 45 = 50 More than 140 8 + 37 = 45 More than 145 9 + 28 = 37 More than 150 12 + 16 = 28 More than 155 14 + 2 = 16 More than 160 2 Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: 34. The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution: Monthly Consumption (in units) 140 160 160 180 180 200 200 220 220 240 240 260 260 - 280 Number of Families 3 8 15 40 50 30 10 y distribution. Sol: The frequency distribution table of more than type is as follows: Height (in cm) (lower class limit) Cumulative frequency (cf) More than 140 3 + 153 = 156 More than 160 8 + 145 = 153 More than 180 15 + 130 = 145 More than 200 40 + 90 = 130 More than 220 50 + 40 = 90 More than 240 30 + 10 = 40 More than 260 10 Taking the lower class limits of on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows: 35. The following table gives the production yield per hectare of wheat of 100 farms of a village. Production Yield (kg/ha) 50 55 55 60 60 65 65- 70 70 75 75 80 Number of farms 2 8 12 24 238 16Read More
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