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Find the median of the given frequency distribution.Class Interval0-1010-2020-3030-4040-50f8791211
Question

Find the median of the given frequency distribution.

Class Interval
0-10
10-20
20-30
30-40
40-50
f
8
7
9
12
11

A.

2159\frac{215}{9}​​

B.

853\frac{85}{3}​​

C.

2659\frac{265}{9}​​

D.

883\frac{88}{3}​​

Correct option is C

Given:

The tabulated data for median

Formula Used:

Median = l+n2cff×h l + \frac{\frac{n}{2} - cf }{f} \times h​​

Where l is the lower limit of median class

n = total number of observations

cf = cumulative frequency

f = frequency of median class

h = class size

Solution:

Class Interval

0-10

10-20

20-30

30-40

40-50

f

8

7

9

12

11

Cumulative Frequency

8

15

24

36

47

Here n = 47 is an odd number

Median class = 47+12=24\frac{47+1}{2} =24​​

Median class = 20-30

Median =20+472159×10= 20 + \frac{\frac{47}{2} - 15 }{9} \times 10​​

=20+23.5159×10= 20 + \frac{23.5 - 15 }{9} \times 10​​

=20+8.59×10= 20 + \frac{8.5 }{9} \times 10​​

=20+859= 20 + \frac{85 }{9}​​

=180+859= \frac{180+85}{9}​​

=2659= \frac{265}{9}​​

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