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Question

Find arithmetic mean of the following frequency distribution by step deviation method.
Variate51015202530frequency204375677245



A
19.09
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B
20.09
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C
30.09
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D
12.09
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Solution

The correct option is D 19.09

1.Choose an arbitrary constant  'a'. (also called assumed mean)

2. xi = Upper limit+Lower limit2

3. Subtract the value of 'a' from xi.

4. The reduced value of (xia) is called the deviation of xi from 'a'.

5. Divide the deviation by constant  where 'h'  is the width of the class interval.

6. ui=xiah

Let the assumed mean be a = 20 and h = 5

VariatefrequencyDeviationui=(xi20)5fiui   (xi)   (fi)di=xi20  5201536010431028615755175206700025725172304510290 N=fi=322  fiui=59

Here,
N=322,a=20,h=5 and fiui=59

Mean=a+fiuif×h
Mean=20+(59322)5
                =200.91
                =19.09


Mathematics

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