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Step7 the point of intersection of the perpendicular

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Unformatted text preview: aw a straight line from the point intersecting 50 116 percent cumulated frequency on the y-axis parallel to the xaxis to intersect the ogive. A perpendicular drawn from this point of intersection on the horizontal axis gives the value of the median. Example 20: Draw an ogive of ‘ less than’ type on the data given below and hence find median. Weight(lbs) Number of persons 8 100-109 15 110-119 21 120-129 34 130-139 45 140-149 26 150-159 20 160-169 15 170-179 10 180-189 6 190-199 Solution: Class interval 100-109 110-119 120-129 130-139 140-149 150-159 160-169 170-179 180-189 190-199 Y No of persons 8 15 21 34 45 26 20 15 10 6 True class interval 99.5-109.5 109.5-119.5 119.5-129.5 129.5-139.5 139.5-149.5 149.5-159.5 159.5-169.5 169.5-179.5 179.5-189.5 189.5-199.5 Less than Ogive 117 Less than c.f 8 23 44 78 123 149 169 184 194 200 X axis 1cm = 10 units Y axis 1cm = 25 units 225 200 175 150 125 N 2 100 75 50 25 Md 99 .5 0 10 9. 50 11 9. 50 12 9. 50 13 9. 50 14 9. 50 15 9. 50 16 9. 50 17 9. 50 18 9. 50 19 9. 50 0 X Example 21: Draw an ogive for the following frequency distribution and hence find median. 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 4 8 12 16 25 10 8 5 2 118 Solution: Class boundary 0 10 20 30 40 50 60 70 80 90 100 Cumulative Frequency Less than More than 95 0 90 5 86 9 78 17 66 29 50 45 25 70 15 80 7 88 2 93 0 95 X axis 1cm = 10units Y axis 1cm = 10units Y 100 Ogives 90 80 70 N 2 60 50 40 30 20 10 Md 0 50 70 80 90 100 101020 20 304040 50 6060 70 80 90 100 30 119 X Merits of Median : 1. Median is not influenced by extreme values because it is a positional average. 2. Median can be calculated in case of distribution with openend intervals. 3. Median can be located even if the data are incomplete. 4. Median can be located even for qualitative factors such as ability, honesty etc. Demerits of Median : 1. A slight change in the series may bring drastic change in median value. 2. In case of even number of items or continuous series, median is an estimate...
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