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