STATISTICS C1

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	8	12	20	28	16	10	6

Calculate the median.

Solution

First we prepare the frequency distribution table.

Class interval	Frequency(f)	Cumulative frequency
15-21	8	8
22-28	12	20
29-35	20	40
36-42	28	68
43-49	16	84
50-56	10	94
57-63	6	100
	∑f = 100

N = 100, N/2=25, Median class must fall in the cumulative frequency of 50. This has to be 36 – 42.

n_b = 40, n_w = 28, 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 + (100/2 – 40)7

                                    28

Median = 35.5 + (50 – 40)7

                                     28

Median = 35.5 + (10)7

                                14

  Median = 35.5 + 70

                                14

  Median = 35.5 +  5

                               

 Median = 40.5

Hence the median is 40.5 

            

TRY THIS…..

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	6	10	18	24	16	10	6

Calculate the median.