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Find the unknown observations from the mean and variance, then the mean deviation

This type of question, asked 5 times: 26 Jun 2022, 11 Apr 2023, 4 Apr 2024, 4 Apr 2025, 28 Jan 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    26 Jun 2022

    78
    The mean of the numbers a,b,8,5,10a,b,8,5,10 is 6 and their variance is 6.8. If MM is the mean deviation of the numbers about the mean, then 25M25M is equal to:

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  2. Question 2

    11 Apr 2023

    165
    Let the mean of 6 observation 1, 2, 4, 5, xx and yy be 5 and their variance be 10 . Then their mean deviation about the mean is equal to

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  3. Question 3

    4 Apr 2024

    73
    Let a,b∈Ra,b \in R. Let the mean and the variance of 6 observations −3,4,7,−6- 3,4,7, - 6, a, b be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:

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  4. Question 4

    4 Apr 2025

    145
    Let the mean and the standard deviation of the observation 2,3,3,4,5,7,a,b2,3,3,4,5,7,a,b be 4 and 2\sqrt{2} respectively. Then the mean deviation about the mode of these observations is :

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  5. Question 5

    28 Jan 2026 S1

    65
    The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are 2,3,5,10,11,13,15,212,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is

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