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Q.

For grouped data, arithmetic mean by assumed mean method is

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a

A +

\sum_{}^{} \frac{d}{N}

b

\sum_{}^{} \frac{fX}{f}

c

A +

\sum_{}^{} \frac{fd}{f}

d

None of these

answer is B.

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Detailed Solution

We have to find the formula for arithmetic mean by assumed mean method for group data.
In the assumed mean approach, any value can be used as the assumed mean regardless of whether it is included in the data; nevertheless, it must be centrally situated in the data in order to simplify the enormous figures and calculate the mean of the given data quickly.
For grouped data, the formula for assumed mean is A +

\sum_{}^{} \frac{fd}{f}

where A is the assumed mean,

\sum_{}^{} fd

is the summation of frequency multiplied with X-A for all figures and

\sum_{}^{} f

is the summation of frequency or the number of elements in the given data.
Thus, A +

\sum_{}^{} \frac{fd}{f}

is the correct formula.
Hence, the correct option is 2.

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