STATISTICS - 2

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	8	16	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	8	18
36-42	16	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 34. This has to be 36 – 42.

n_b = 18, n_w = 16, 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 – 18)7

                            16

Median = 35.5 + (25 – 20)7

                             16

Median = 35.5 + (5)7

                        16

  Median = 35.5 +  35

                           16

  Median = 35.5 +  2.1875

                               

 Median = 37.6875

Hence the median is 37.69 ( to 2d.p)                     

 

TRY THIS...........

Distribution of Kiswahili test marks was given as hereunder. 

Length(mm)	10 - 19	20- 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79
Frequency	3	7	9	15	8	5	3

Calculate the median.