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Marks number of students 70 greater than 10 62

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Unformatted text preview: 38 40 46 30 6 50-60 53 24 7 60-70 61 17 8 70-80 66 9 5 80-90 70 4 4 90-100 70 70 N = = 35 2 2 114 N 2 −m xc Median = l + f 35 − 32 = 40 + × 10 8 = 40 +3.75 = 43.75 Example 19: Compute median for the following data. Mid-Value 5 15 25 35 45 55 65 75 Frequency 7 10 15 17 8 4 6 7 Solution : Here values in multiples of 10, so width of the class interval is 10. Mid x 5 15 25 35 45 55 65 75 C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 f 7 10 15 17 8 4 6 7 74 74 N = = 37 2 2 N − m 2 ×c Median = l + f 115 c.f 7 17 32 49 57 61 67 74 37 − 32 = 30 + × 10 17 = 30 + 2.94 = 32.94 Graphic method for Location of median: Median can be located with the help of the cumulative frequency curve or ‘ ogive’ . The procedure for locating median in a grouped data is as follows: Step1: The class boundaries, where there are no gaps between consecutive classes, are represented on the horizontal axis (x-axis). Step2: The cumulative frequency corresponding to different classes is plotted on the vertical axis (y-axis) against the upper limit of the class interval (or against the variate value in the case of a discrete series.) Step3: The curve obtained on joining the points by means of freehand drawing is called the ‘ ogive’ . The ogive so drawn may be either a (i) less than ogive or a (ii) more than ogive. N N +1 Step4: The value of or is marked on the y-axis, where 2 2 N is the total frequency. N Step5: A horizontal straight line is drawn from the point or 2 N +1 on the y-axis parallel to x-axis to meet the ogive. 2 Step6: A vertical straight line is drawn from the point of intersection perpendicular to the horizontal axis. Step7: The point of intersection of the perpendicular to the x-axis gives the value of the median. Remarks : 1. From the point of intersection of ‘ less than’ and ‘ more than’ ogives, if a perpendicular is drawn on the x-axis, the point so obtained on the horizontal axis gives the value of the median. 2. If ogive is drawn using cumulated percentage frequencies, then we dr...
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