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Find the unknown observations from the given mean and variance

This type of question, asked 13 times: 2021 Paper 11, 2021 Paper 12, 2021 Paper 16, 2021 Paper 19, 27 Jun 2022, 1 Feb 2023, 8 Apr 2023, 29 Jan 2024, 31 Jan 2024, 2 Apr 2025, 3 Apr 2025, 23 Jan 2026 S1, 6 Apr 2026 S2. All 13 questions below, oldest first.

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  1. Question 1

    2021 Paper 11

    44
    The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2 , 4,5 and 7 , then the remaining two observations are:

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  2. Question 2

    2021 Paper 12

    53
    If the mean and variance of six observations 7,10,11,15,a,b7,10,11,15,a,b are 10 and 203\frac{20}{3}, respectively, then the value of ∣a−b∣|a - b| is equal to:

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  3. Question 3

    2021 Paper 16

    51
    For the data 6,10,7,13,a,12,b,126,10,7,13,a,12,b,12. If mean is 9 , variance is 374\frac{37}{4} find (a−b)2(a-b)^{2}.

  4. Question 4

    2021 Paper 19

    88
    Let the mean and variance of four numbers 3,7,x3,7,x and y(x>y)y(x>y) be 5 and 10 respectively. Then the mean of four numbers 3+2x,7+2y,x+y3 + 2x,7 + 2y,x+y and x−yx - y is

  5. Question 5

    27 Jun 2022

    166
    The mean and variance of the data 4,5,6,6,7,8,x,y4,5,6,6,7,8,x,y where x<yx < y are 6 , and 94\frac{9}{4} respectively. Then x4+y2x^{4}+y^{2} is equal to

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  6. Question 6

    1 Feb 2023

    70
    The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3,5 then the sum of cubes of the remaining two observations is

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  7. Question 7

    8 Apr 2023

    90
    Let the mean and variance of 8 numbers x,y,10x,y,10, 12,6,12,4,812,6,12,4,8, be 9 and 9.25 respectively. If x>yx > y, then 3x−2y3x - 2y is equal to

  8. Question 8

    29 Jan 2024

    87
    If the mean and variance of the data 65,68,58,4465,68,58,44, 48,45,60,α,β,6048,45,60,\alpha,\beta,60 where α>β\alpha > \beta are 56 and 66.2 respectively, then α2+β2\alpha^{2}+\beta^{2} is equal to

  9. Question 9

    31 Jan 2024

    162
    Let the mean and the variance of 6 observation a, b,68,44,48,60b,68,44,48,60 be 55 and 194, respectively if a>ba > b, then a+3ba + 3b is

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  10. Question 10

    2 Apr 2025

    136
    If the mean and the variance of 6,4,a,8,b,12,106,4,a,8,b,12,10, 13 are 9 and 9.25 respectively, then a+b+aba+b+ab is equal to :

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  11. Question 11

    3 Apr 2025

    129
    Let the Mean and Variance of five observations x1=1,x2=3,x3=a,x4=7x_{1}= 1,x_{2}= 3,x_{3}= a,x_{4}= 7 and x5=b,a>bx_{5}=b,a>b, be 5 and 10 respectively. Then the Variance of the observations n+xn, n=1,2,…,5n +x_{n},\ n = 1,2,\ldots,5 is

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  12. Question 12

    23 Jan 2026 S1

    63
    Let the mean and variance of 8 numbers −10,−7,−1,x,y,9,2,16- 10, - 7, - 1,x,y,9,2,16 be 72\frac{7}{2} and 2934\frac{293}{4}, respectively. Then the mean of 4 numbers x,y,x+y+1,∣x−y∣x,y,x + y + 1,|x - y| is:

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  13. Question 13

    6 Apr 2026 S2

    58
    Let the mean and the variance of seven observations 2,4,α,8,β,12,14,α<β2,4,\alpha,8,\beta,12,14,\alpha<\beta, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α+23\alpha+ 2 and 2β+12\beta+ 1 is :

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