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New mean or variance when every observation is multiplied by, or increased by, a constant

This type of question, asked 6 times: May 2022 S1, 9 May 2023 S2, 10 May 2023 S1, 10 May 2024 S2, 11 May 2024 S1, 14 May 2024 S1. All 6 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    119
    The variance and mean of 15 observations are respectively 6 and 10. If each observation is increased by 8 then the new variance and new mean of resulting observations are respectively

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  2. Question 2

    9 May 2023 S2

    120
    The variance of 20 observations is 5. If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observations is

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  3. Question 3

    10 May 2023 S1

    148
    Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

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  4. Question 4

    10 May 2024 S2

    115
    Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

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  5. Question 5

    11 May 2024 S1

    140
    If variance of x1,x2,…,xnx_1, x_2, \ldots, x_n is σx2\sigma_x^2, then the variance of λx1,λx2,…,λxn\lambda x_1, \lambda x_2, \ldots, \lambda x_n (λ≠0)(\lambda \neq 0) is

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  6. Question 6

    14 May 2024 S1

    150
    The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

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