STATISTICS B8

Distribution of Chinese language test marks was given as hereunder.

Length(mm)	10 - 19	20- 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79
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
10-19	3	3
20-29	5	8
30-39	9	17
40-49	12	29
50-59	6	35
60-69	3	38
70-79	2	40
	∑f = 40

N = 40, N/2=20, Median class must fall in the cumulative frequency of 20. This has to be 40 – 49.

n_b = 17, n_w = 12, 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 + (40/2 – 17)10

                                     12

Median = 39.5 + (20 – 17)10

                                     12

Median = 39.5 + (3)10

                                12

  Median = 39.5 + 30

                              12

  Median = 39.5 +  2.5

                               

 Median = 42

Hence the median is 42