STATISTICS B6

Distribution of Kiswahili test marks was given as heeunder.

Length(mm)	10 - 19	20- 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79
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
10-19	4	4
20-29	6	10
30-39	10	20
40-49	14	34
50-59	8	42
60-69	5	47
70-79	3	50
	∑f = 50

N = 50, N/2=25, Median class must fall in the cumulative frequency of 25. This has to be 40 – 49.

n_b = 20, n_w = 14, Upper boundary(U)= 49.5, Lower boundary(L) =39.5

i = Upper boundary – Lower boundary

i = 49.5 – 39.5

i = 10

Median = L + (N/2 – n_b)i/n_w

                              

Median = 39.5 + (50/2 – 20)10

                                     14

Median = 39.5 + (25 – 20)10

                                     14

Median = 39.5 + (5)10

                                14

  Median = 39.5 + 50

                                14

  Median = 39.5 +  3.57

                               

 Median = 43.07

Hence  median is 43.07