Friday 10 January 2014

STATISTICS B11



Distribution of English test marks was given as hereunder.

Length(mm)
20 - 27
28- 35
36 - 43
44-51
52 - 59
60 - 67
68 - 75
Frequency
3
5
9
12
6
3
2

Calculate the median.

Solution







Class interval
Frequency(f)
Cumulative frequency
20 - 27
5
5
28- 35
7
12
36 - 43
10
22
44 - 51
12
34
52 - 59
8
42
60 - 67
5
47
68 - 75
3
50

∑f = 50





N = 45, N/2=22.5, Median class must fall in the cumulative frequency of 25. This has to be 44 – 51.

nb = 22, nw = 12, Upper boundary(U)= 51.5, Lower boundary(L) =43.5


i = Upper boundary – Lower boundary
i = 51.5 – 43.5
i = 8

Median = L + (N/2 – nb)i/nw
                              

Median = 43.5 + (50/2 – 22)8
                                  12

Median = 43.5 + (25 – 22)8
                                 12

Median = 43.5 + (3)8
                             12

Median = 43.5 + 24
                           12

Median = 43.5 +  2
                               
Median = 43.5

Hence the median is 43.5

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