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New mean after adding a constant to or multiplying every observation

This type of question, asked 3 times: CDS 2 2025, CDS 1 2026, CDS 2 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2025

    94
    The arithmetic mean of 200 observations is 60. If 5 is multiplied to each observation, then what will be the new arithmetic mean?

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  2. Question 2

    CDS 1 2026

    38
    The arithmetic mean of 100 observations is 50. If 10 is added to each observation then what will be the new arithmetic mean ?

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  3. Question 3

    CDS 2 2026

    97
    If the mean of 15 observations, namely x1,x2,x3,…,x15x_1, x_2, x_3, \ldots, x_{15} is 2.5, then what is the value of ∑i=115[5(4xi+1)]\sum_{i=1}^{15} [5(4x_i + 1)] ?

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