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Measures of Dispersion

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type 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. This one: 14 May 2024 S1 See all 6 of this type

    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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  2. Question 2

    This type asked 5 times: 4 May 2023 S2, 10 May 2023 S2, 15 May 2023 S1, 16 May 2023 S2, 9 May 2024 S2. This one: 9 May 2024 S2 See all 5 of this type

    107
    If the mean and S.D. of the data 3,5,7,a,b3, 5, 7, a, b are 5 and 2 respectively, then aa and bb are the roots of the equation

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  3. Question 3

    This type asked 4 times: May 2021 S1, 4 May 2023 S1, 15 May 2023 S2, 13 May 2024 S2. This one: 13 May 2024 S2 See all 4 of this type

    105
    Variance of first 2n2n natural numbers is

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  4. Question 4

    Asked 3 times: 4 May 2023 S2*, 10 May 2023 S2*, 16 May 2023 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    118
    The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, then the product of remaining two observations is

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  5. Question 5

    Asked 2 times: 11 May 2024 S2, 14 May 2024 S2 See all 2 times it was asked

    149
    If both mean and variance of 50 observations x1,x2,…,x50x_1, x_2, \ldots, x_{50} are equal to 16 and 256 respectively, then mean of (x1−5)2,(x2−5)2,…,(x50−5)2(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2 is

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  6. Question 6

    Asked 2 times: 10 May 2023 S1*, 10 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    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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  7. Question 7

    This type asked 2 times: 16 May 2023 S1, 12 May 2024 S2. This one: 12 May 2024 S2 See all 2 of this type

    149
    For 20 observations of variable xx, if ∑(xi−2)=20\sum(x_i-2)=20 and ∑(xi−2)2=100\sum(x_i-2)^2=100, then the standard deviation of variable xx is

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  8. Question 8

    This type asked 2 times: May 2021 S1, 2 May 2023 S1. This one: 2 May 2023 S1 See all 2 of this type

    145
    The mean of 100 observations is 50 and their standard deviation is 5, then the sum of all squares of all the observations is

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  9. Question 9

    Asked once: 11 May 2024 S1 (same type asked 6 times) See all 6 of this type

    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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  10. Question 10

    Asked once: 15 May 2023 S1 (same type asked 5 times) See all 5 of this type

    149
    The mean of the numbers a,b,8,5,10a,b,8,5,10 is 6 and the variance is 6.8. Then which of the following gives possible values of aa and bb?

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