Let and where gt be the means of two sets comprising 1 n and 2 n where n2 lt n1 observatio...........

Quantitative Aptitude (CDS) Arithmetic progression

Let $\small \bar X1$ and $\small \bar X2$ (where $\small \bar X2$ > $\small \bar X1$ ) be the means of two sets comprising 1 n and 2 n (where n₂ < n₁ ) observations respectively. If $\small \bar X$ is the mean when they are pooled, then which one of the following is correct?

$\small \bar X1 < \bar X < \bar X2$

$\small \small \bar X1 > \bar X2$

$\small \small \bar X < \bar X1$

$\small (\bar X1-\bar X2)+( \bar X2 - \bar X) = 0$

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Explanation:

Since $\small \bar X2 > \bar X1$
On pooling n1 & n2, the larger set of observation( n₁+ n₂) will have a mean lower than $\small \bar X2$ (because of n, observations) but more than $\small \bar X1$ (because of n2 observations terms). Thus, it will be in between $\small \bar X2\: and\: \bar X1$ .