PYQ Vault
EbooksTutor

Mean, variance or mean deviation of an AP or of the first n natural numbers

This type of question, asked 8 times: 2021 Paper 20, 25 Jun 2022, 24 Jan 2023, 30 Jan 2023, 1 Feb 2023, 23 Jan 2025, 22 Jan 2026 S2, 24 Jan 2026 S2. All 8 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 20

    87
    Let nn be an odd natural number such that the variance of 1,2,3,4,…,n1,2,3,4,\ldots,n is 14 . Then nn is equal to

  2. Question 2

    25 Jun 2022

    175
    If the mean deviation about the mean of the numbers 1,2,3,…..,n1,2,3,\ldots..,n, where nn is odd, is 5(n+1)n\frac{5(n + 1)}{n}, then nn is equal to

  3. Question 3

    24 Jan 2023

    164
    Let the six numbers a1,a2,a3,a4,a5,a6a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}, be in A.P. and a1+a3=10a_{1}+a_{3}= 10. If the mean of these six numbers is 192\frac{19}{2} and their variance is σ2\sigma^{2}, then 8σ28\sigma^{2} is equal to:

    Tap an option to check your answer.

  4. Question 4

    30 Jan 2023

    157
    Let SS be the set of all values of a1a_{1} for which the mean deviation about the mean of 100 consecutive positive integers a1,a2,a3,….a100a_{1},a_{2},a_{3},\ldots.a_{100} is 25. Then SS is

    Tap an option to check your answer.

  5. Question 5

    1 Feb 2023

    169
    Let 9=x1<x2<…<x79 =x_{1}<x_{2}< \ldots <x_{7} be in an A.P. with common difference dd. If the standard deviation of x1,x2,…,x7x_{1},x_{2},\ldots,x_{7} is 4 and mean is x‾\overline{x}, then x‾+x6\overline{x}+x_{6} is equal to:

    Tap an option to check your answer.

  6. Question 6

    23 Jan 2025

    149
    The variance of the numbers 8,21,34,47,…,3208,21,34,47,\ldots,320, is ____\_\_\_\_

  7. Question 7

    22 Jan 2026 S2

    52
    If the mean deviation about the median of the numbers k,2k,3k,….,1000kk,2k,3k,\ldots.,1000k is 500 , then k2k^{2} is equal to :

    Tap an option to check your answer.

  8. Question 8

    24 Jan 2026 S2

    64
    Let X={x∈N:1≤x≤19}X = \{ x \in N:1 \leq x \leq 19\} and for some a,b∈Ra,b \in R, Y={ax+b:x∈X}Y = \{ ax + b:x \in X\}. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of bb is

    Tap an option to check your answer.