Question

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

A
19.09
B
20.09
C
30.09
D
12.09

Solution

## The correct option is D 19.091.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 (xi−a) 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=xi−ah Let the assumed mean be a = 20 and h = 5 VariatefrequencyDeviationui=(xi−20)5fiui   (xi)   (fi)di=xi−20  520−15−3−601043−10−2−861575−5−1−75206700025725172304510290 N=∑fi=322  ∑fiui=−59 Here, N=322,a=20,h=5 and ∑fiui=−59 ∴Mean=a+∑fiui∑f×h ⇒Mean=20+(−59322)5                 =20−0.91                 =19.09 Mathematics

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