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Mean

If x̅̅1̅, x̅̅...

Question

If $_{1},_{2} \dots,_{n}$ are the means of n groups with $n_{1}, n_{2}, \dots, n_{n}$ number of observations respectively then the mean $¯ x$ of all the groups taken together is
(a) $\sum_{n}^{i = 1} n,_{i}$

(b) $\frac{\sum_{i = 1}^{n} n_{i}_{i}}{n^{2}}$

(c) $\frac{\sum_{i = 1}^{n} n_{i}_{i}}{\sum_{i = 1}^{n} n_{i}}$

(d) $\frac{\sum_{i = 1}^{n} n_{i} {¯ x}_{i}}{2 n}$

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Solution

ANSWER:
(c) ∑ni=1ni¯xi∑ni=1ni

Sum of all terms=n1x ̄1+n2x ̄2+...nnx ̄n
Number of terms=(n1+n2+...nn)

∴Mean=(∑ni=1ni¯xi∑ni=1ni

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