STATISTICS C4

Distribution of Civics test marks was given as here-under.  

Marks	10 - 19	20- 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79
Frequency	3	5	8	11	6	4	3

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	8	16
40-49	11	27
50-59	6	33
60-69	4	37
70-79	3	40
	∑f = 40

N = 40, N/2=20, Median class must fall in the cumulative frequency of 27. This has to be 40 – 49.

n_b = 16, n_w = 11, 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 – 16)10

                                11

Median = 39.5 + (20 – 16)10

                               11

Median = 39.5 + (4)10

                          11

Median = 39.5 + 40

                           11

Median = 39.5 +  3.67

                               

Median = 43.17

Hence the median is 43.17           


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

Distribution of Biology test marks was given as here-under.  

Marks	10 - 19	20- 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79
Frequency	3	6	10	15	8	5	3

Calculate the median.