STATISTICS B7

Distribution of Biology test marks was given as hereunder.

Length(mm)	15 - 19	20- 24	25 - 29	30 - 34	35 - 39	40 - 44	45 - 49
Frequency	3	5	9	12	6	3	2

Calculate the median.

Solution

First we prepare the frequency distribution table.

Class interval	Frequency(f)	Cumulative frequency
15-19	3	3
20- 24	5	8
25 - 29	9	17
30 - 34	12	29
35 - 39	6	35
40 - 44	3	38
45 - 49	2	40
	∑f = 40

N = 40, N/2=20, Median class must fall in the cumulative frequency of 20. This has to be 30 – 34.

n_b = 17, n_w = 12, Upper boundary(U)= 34.5, Lower boundary(L) =29.5

 i = Upper boundary – Lower boundary

i = 34.5 – 29.5

i = 5

Median = L + (N/2 – n_b)i/n_w

                              

Median = 29.5 + (40/2 – 17)5

                                     12

Median = 29.5 + (20 – 17)5

                                  12

Median = 29.5 + (3)5

                             12

  Median = 29.5 + 15

                             12

  Median = 29.5 +  1.25

                               

 Median = 30.75

Hence the median is 30.75