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Question

If the median of the distribution is given below is 28.5, find the values of x and y. Class interval Frequency 0 − 10 5 10 − 20 x 20 − 30 20 30 − 40 15 40 − 50 y 50 − 60 5 Total 60

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Solution

The cumulative frequency for the given data is calculated as follows. Class interval Frequency Cumulative frequency 0 − 10 5 5 10 − 20 x 5+ x 20 − 30 20 25 + x 30 − 40 15 40 + x 40 − 50 y 40+ x + y 50 − 60 5 45 + x + y Total (n) 60 From the table, it can be observed that n = 60 45 + x + y = 60 x + y = 15 (1) Median of the data is given as 28.5 which lies in interval 20 − 30. Therefore, median class = 20 − 30 Lower limit (l) of median class = 20 Cumulative frequency (cf) of class preceding the median class = 5 + x Frequency (f) of median class = 20 Class size (h) = 10 From equation (1), 8 + y = 15 y = 7 Hence, the values of x and y are 8 and 7 respectively.

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