Tuesday 1 July 2014

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.

nb = 18, nw = 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 – nb)i/nw
                              

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.

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