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Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?

Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct? Correct Answer x̅<sub>1</sub> &lt; x̅ &lt; x̅<sub>2</sub>

Pooled mean is simply known as the weighted mean

Hence, when the two means are pooled,

Pooled mean = x̅ = (n1x̅1 + n2x̅2)/(n1 + n2)

⇒ x̅ = n1x̅1/(n1 + n2) + n2x̅2/(n1 + n2)

∵ n1 > n2

The first term will be nearly equal to x̅1 and the second term will be less than x̅2

∴ x̅1 < x̅ < x̅2

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