STATISTICS B4

Distribution of length of nails in mm is as shown below.

Length(mm)	15 - 21	22- 28	29 - 35	36 - 42	43 - 49	50 - 56	57 - 63
Frequency	4	6	10	14	8	5	3

Calculate the median.

Solution

First we prepare the frequency distribution table.

Class interval	Frequency(f)	Cumulative frequency
15-21	4	4
22-28	6	10
29-35	10	20
36-42	14	34
43-49	8	42
50-56	5	47
57-63	3	50
	∑f = 50

N = 50, N/2=25, Median class must fall in the cumulative frequency of 25. This has to be 36 – 42.

n_b = 20, n_w = 14, Upper boundary(U)= 42.5, Lower boundary(L) =35.5

i = Upper boundary – Lower boundary

i = 42.5 – 35.5

i = 7

Median = L + (N/2 – n_b)i/n_w

                              

Median = 35.5 + (50/2 – 20)7

                                     14

Median = 35.5 + (25 – 20)7

                                   14

Median = 35.5 + (5)7

                             14

Median = 35.5 + 5

                              2

Median = 35.5 +  2.5

               

                

Median = 38

Hence  median is 38