JEE Mathematics

Measures of Dispersion: JEE Questions & Solutions

30 previous-year JEE Mathematics questions on Measures of Dispersion, each with a worked step-by-step solution.

Intermediate

Previous-year questions

  1. 01If the mean deviation about the median of the numbers k, 2k, 3k, …, 1000k is 500, then k² is equal toMCQMediumJEE 2026
  2. 02Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be 7/2 and 293/4, respectively. Then the mean of 4 numbers x, y, x+y+1,…MCQMediumJEE 2026
  3. 03Let X={x∈ℕ:1≤ x≤19} and for some a,b∈ℝ, Y={ax+b:x∈ X}. If the mean and variance of the elements of Y are 30 and 750 respectively, then the…MCQMediumJEE 2026
  4. 04The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the…MCQMediumJEE 2026
  5. 05The variance of the numbers 8, 21, 34, 47, …, 320, is:NVAMediumJEE 2025
  6. 06For a statistical data x₁, x₂, …, x₁₀ of 10 values, a student obtained the mean as 5.5 and Σ_(i=1)¹⁰ xᵢ² = 371. He later found that he had…MCQEasyJEE 2025
  7. 07If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to:MCQMediumJEE 2025
  8. 08Let the Mean and Variance of five observations xᵢ, i = 1, 2, 3, 4, 5 be 5 and 10 respectively. If three observations are x₁ = 1, x₂ = 3, x₃…MCQMediumJEE 2025
  9. 09Let the mean and the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and √2 respectively. Then the mean deviation about…MCQMediumJEE 2025
  10. 10The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40.…MCQMediumJEE 2025
  11. 11Let a₁, a₂, …, a₁₀ be 10 observations with Σ a_k = 50 and Σ (a_k · a_j) = 1100. Find the standard deviation.MCQMediumJEE 2024
  12. 12The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking, it was found that an observation…NVAMediumJEE 2024
  13. 13The variance σ² of the data is: xᵢ: 0, 1, 5, 6, 10, 12, 17 fᵢ: 3, 2, 3, 2, 6, 3, 3NVAMediumJEE 2024
  14. 14Let the median and the mean deviation about the median of 7 observations 170, 125, 230, 190, 210, a, b be 170 and 205/7 respectively. Then…MCQMediumJEE 2024
  15. 15The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, an observation was mistakenly…MCQMediumJEE 2024
  16. 16If the variance of the frequency distribution given below is 160, then the value of c ∈ ℕ is: | x | c | 2c | 3c | 4c | 5c | 6c |…MCQMediumJEE 2024
  17. 17Let the six numbers a₁, a₂, a₃, a₄, a₅, a₆ be in A.P., and a₁ + a₃ = 10. If the mean of these six numbers is 19/2 and their variance is σ²,…MCQMediumJEE 2023
  18. 18The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is…MCQMediumJEE 2023
  19. 19If the variance of the frequency distribution xᵢ 2 3 4 5 6 7 8 fᵢ 3 6 16 α 9 5 6 is 3, then α is equal to:NVAMediumJEE 2023
  20. 20Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α > 0, and the mean and standard deviation…MCQMediumJEE 2023
  21. 21The 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…MCQMediumJEE 2023
  22. 22Let 9 = x₁ < x₂ < … < x₇ be in an A.P. with common difference d. If the standard deviation of x₁, x₂, …, x₇ is 4 and the mean is x, then x…MCQMediumJEE 2023
  23. 23The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and σ²…MCQMediumJEE 2023
  24. 24If the mean and variance of the frequency distribution | xᵢ | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | |---|---|---|---|---|---|---|---|---| |…NVAMediumJEE 2023
  25. 25Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8 be 9 and 9.25 respectively. If x > y, then 3x - 2y is equal to:NVAMediumJEE 2023
  26. 26Let m be the mean and σ be the standard deviation of the distribution: | xᵢ | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | fᵢ |…MCQMediumJEE 2023
  27. 27Let the mean of 6 observations 1, 2, 4, 5, x, and y and their variance be 10. Then their mean deviation about the mean is equal to:MCQMediumJEE 2023
  28. 28Let the positive numbers a₁, a₂, a₃, a₄, and a₅ be in a G.P. Let their mean and variance be 31/10 and m/n, respectively, where m and n are…NVAMediumJEE 2023
  29. 29The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks…NVAMediumJEE 2023
  30. 30The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded…MCQMediumJEE 2023

Frequently asked questions

Our bank has 30 previous-year JEE Mathematics questions tagged to Measures of Dispersion, drawn from JEE papers between 2023 and 2026, including 4 from 2026 alone. Each comes with a full step-by-step solution.

Measures of Dispersion is rated Intermediate overall for JEE Mathematics. The PYQs on this page break down as 29 medium, 1 easy.

Of the 30 previous-year questions on Measures of Dispersion, 22 are multiple-choice (MCQ) and 8 are numerical-value (NVA) questions.

Based on recent paper analysis, Measures of Dispersion is worth about 2 marks in JEE Main. It sits in Statistics & Probability, a Class 11 Mathematics chapter.

More Statistics & Probability topics

Probability Basics32Probability Distributions21Conditional Probability & Bayes Theorem15Measures of Central Tendency10

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