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If the median of a distribution given below is 28.5 then, find the value of x & y.

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If the median of a distribution given below is 28.5 then, find the value of x & 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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Given data, n = 60

Median of the given data = 28.5

Where, n/2 = 30

Median class is 20 – 30 with a cumulative frequency = 25 + x

Lower limit of median class, l = 20

Cf = 5 + x

f = 20 & h = 10

Median = \(l + (\frac{\frac{n}{2} - C_f}{f}) \times h \)

Substitute the values

28.5 = 20 + ((30 − 5 − x)/20) × 10

8.5 = (25 – x)/2

17 = 25-x

Therefore, x =8

Now, from cumulative frequency, we can identify the value of x + y as follows:

60 = 5 + 20 + 15 + 5 + x + y

Now, substitute the value of x, to find y

60 = 5 + 20 + 15 + 5 + 8 + y

y = 60 - 53

y = 7

Therefore, the value of x = 8 and y = 7.

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