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Combined mean of groups

This type of question, asked 2 times: CDS 2 2018, CDS 2 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    59
    Let xˉ1\bar{x}_1 and xˉ2\bar{x}_2 (where xˉ2>xˉ1\bar{x}_2 > \bar{x}_1) be the means of two sets comprising n1n_1 and n2n_2 (where n2<n1n_2 < n_1) observations respectively. If xˉ\bar{x} is the mean when they are pooled, then which one of the following is correct ?

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  2. Question 2

    CDS 2 2025

    95
    A distribution consists of 3 components with frequencies 45, 40 and 55 having their means 2, 2.5 and 2 respectively. What is the mean of the combined distribution?

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