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Some observations are removed: mean and variance of the rest

This type of question, asked 6 times: 2021 Paper 23, 29 Jun 2022, 26 Jul 2022, 30 Jan 2023, 29 Jan 2024, 2 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 23

    80
    The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is:

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  2. Question 2

    29 Jun 2022

    80
    Let the mean and the variance of 5 observations x1,x2,x3,x4,x5x_{1},x_{2},x_{3},x_{4},x_{5} be 245\frac{24}{5} and 19425\frac{194}{25} respectively. If the mean and variance of the first 4 observation are 72\frac{7}{2} and aa respectively, then (4a+x5)\left( 4a +x_{5} \right) is equal to:

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  3. Question 3

    26 Jul 2022

    176
    The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ\sigma is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ238\sigma^{2} is equal to

  4. Question 4

    30 Jan 2023

    88
    The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and aa and bb are respectively mean and variance of remaining 6 observation, then a+3b−5a + 3b - 5 is equal to

  5. Question 5

    29 Jan 2024

    154
    If the mean and variance of five observations are 245\frac{24}{5} and 19425\frac{194}{25} respectively and the mean of first four observations is 72\frac{7}{2}, then the variance of the first four observations is equal to

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  6. Question 6

    2 Apr 2026 S2

    59
    The mean and variance of nn observations are 8 and 16, respectively. If the sum of the first ( n−1n- 1 ) observations is 48 and the sum of squares of the first ( n−1n - 1 ) observations is 496 , then the value of n is :

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