Question

40. Calculate the median for the following frequency distribution:
Class interval 1-4 5-8 9-12 13-16 17-20 21-24 25-28 29-32 33-36 37-40
Frequency | 2 5 | 8 | 9 | 12 | 14 | 14 | 15 | 11 | 13​

Answer 1

Answer:

The median of this frequency distribution is 24.9285

Step-by-step explanation:

Let's write down the formula for getting the median for grouped data:

Median = L + $(\frac{\frac{N}{2} - F}{f})$C

Where:

L = Lower limit for the median class.

N = Total number of entries

F = Cumulative before the median class.

f = frequency of the median group

C = class boundary

∑ frequency = 121

N = 103

N/2 = 51.50

The cumulative frequencies for the classes are:

Class                                          C.F

1 - 4                                             2

5 - 8                                            7

9 - 12                                           15

13 - 16                                          24

17 - 20                                         36                                      

21 - 24                                          50

25 - 28                                         64

29 - 32                                          79

33 - 36                                           90

37 - 40                                           103

Since N/2 = 51.50, the median class is 25 - 28

Now:

L = 24.5 (lower class limit of median class)

F = 50

f = 14

C = 4

Doing the substitution we have:

Median =24.5 + {(51.50 - 50)/14} × 4

= 24.5 + 0.4285 = 24.9285