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Mathematics - Statistics

Practise 164 JEE Main previous year questions on Statistics, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Statistics has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 164 questions in all. 48% of them were easy, 48% moderate and 4% tough. Most of its questions came from 2023, with 21 questions that year. In the last three years (2024–2026) it had 32 questions across 49 papers, about 0.7 per paper.

The chapter's 8 topics are not weighted equally: Measures of Dispersion (108 questions, 66%), Mean (25 questions, 15%), and Mean Square Deviation (11 questions, 7%) have been asked the most. Measures of Dispersion has also led over the last five years, with 56 questions. Measures of Dispersion has produced the most tough questions (4).

  1. 1A set of four observations has mean and variance . Another set of six observations has mean and variance . Then, the variance of all these o08 Apr, 2026 (E)Measures of Dispersion
  2. 2A data consists of observations . If and , then the ratio of mean to standard deviation of this data is:06 Apr, 2026 (M)Mean
  3. 3Let the mean and the variance of seven observations , , be and respectively. Then the quadratic equation whose roots are and is :06 Apr, 2026 (E)Measures of Dispersion
  4. 4The mean deviation about the mean for the data is equal to:05 Apr, 2026 (M)Mean
  5. 5A variable takes values with frequencies , respectively. If the mean of this data is , then its median is :05 Apr, 2026 (E)Mean
  6. 6Suppose that the mean and median of the non-negative numbers , are and , respectively. If the mean deviation about the median is , then is e04 Apr, 2026 (M)Mean
  7. 7For observations , if and , then their standard deviation is:04 Apr, 2026 (E)Measures of Dispersion
  8. 8If the mean of the data Class Frequency is , then is one of the roots of the equation :02 Apr, 2026 (M)Mean
  9. 9The mean and variance of observations are and , respectively. If the sum of the first observations is and the sum of squares of the first ob02 Apr, 2026 (E)Mean
  10. 10The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are , then the mean deviation about the me28 Jan, 2026 (M)Measures of Dispersion
  11. 11The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations in this data is replaced by , then the mea24 Jan, 2026 (M)Measures of Dispersion
  12. 12Let and for some . If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of is24 Jan, 2026 (E)Mean
  13. 13Let the mean and variance of 8 numbers be and , respectively. Then the mean of 4 numbers is :23 Jan, 2026 (M)Measures of Dispersion
  14. 14If the mean and the variance of the data \( {array}{|c|c|c|c|c|} {Class} & 4 {-}8 & 8 {-}12 & 12 {-}16 & 16 {-}20 \\ {Frequency} & 3 & & 4 &23 Jan, 2026 (E)Measures of Dispersion
  15. 15If the mean deviation about the median of the numbers is 500, then is equal to :22 Jan, 2026 (E)Measures of Dispersion
  16. 16Let the mean and variance of 7 observations , be 8 and 16 respectively. Two numbers are chosen from one after another without replacement, t21 Jan, 2026 (M)Mean
  17. 17The mean and standard deviation of 100 observations are 40 and 5.1 , respectively, By mistake one observation is taken as 50 instead of 40. 07 Apr, 2025 (M)Measures of Dispersion
  18. 18Let the mean and the standard deviation of the observation , a, b be 4 and respectively. Then the mean deviation about the mode of these obs04 Apr, 2025 (E)Measures of Dispersion
  19. 19Let the Mean and Variance of five observations and , be 5 and 10 respectively. Then the Variance of the observations is03 Apr, 2025 (E)Measures of Dispersion
  20. 20If the mean and the variance of , 13 are 9 and 9.25 respectively, then is equal to :02 Apr, 2025 (E)Measures of Dispersion
  21. 21Let \(x_1, x_2, , x_{10}\) be ten observations such that \( _{i=1}^{10} (x_i-2 )=30, _{i=1}^{10} (x_i- )^2=98, 2\), and their variance is \(29 Jan, 2025 (M)Measures of Dispersion
  22. 22For a statistical data of 10 values, a student obtained the mean as 5.5 and . He later found that he had noted two values in the data incorr24 Jan, 2025 (M)Measures of Dispersion
  23. 23Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this g23 Jan, 2025 (M)Median
  24. 24The variance of the numbers is23 Jan, 2025 (E)Measures of Dispersion
  25. 25The frequency distribution of the age of students in a class of 40 students is given below. If the mean deviation about the median is 1.25, 09 Apr, 2024 (M)Relation Between Variance and Mean Deviation
  26. 26If the variance of the frequency distribution is 160, then the value of is09 Apr, 2024 (E)Relation Between Variance and Mean Deviation
  27. 27Let and . Let the mean, the mean deviation about the mean and the variance of the 5 observations be 18,4 and , respectively. Then is equal t08 Apr, 2024 (E)Relation Between Variance and Mean Deviation
  28. 28The mean and standard deviation of 20 observations are found to be 10 and 2 . respectively. On rechecking, it was found that an observation 06 Apr, 2024 (M)Mean Square Deviation
  29. 29From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable denote the number o05 Apr, 2024 (M)Relation Between Variance and Mean Deviation
  30. 30Let the mean and the standard deviation of the probability distribution be and , respectively. If , then is equal to________05 Apr, 2024 (E)Relation Between Variance and Mean Deviation
  31. 31Let . Let the mean and the variance of 6 observations be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations 04 Apr, 2024 (M)Relation Between Variance and Mean Deviation
  32. 32If the mean of the following probability distribution of a random variable : is , then the variance of the distribution is04 Apr, 2024 (E)Relation Between Variance and Mean Deviation
  33. 33Let the median and the mean deviation about the median of 7 observation 170 , 125 , 230 , 190 , 210 , a , b be 170 and 205 7 respectively. T01 Feb, 2024 (M)Measures of Dispersion
  34. 34Consider 10 observation x 1 , x 2 , . .. x 10 , such that ∑ i = 1 10 x i − α = 2 and ∑ i = 1 10 x i − β 2 = 40 , where α , β are positive in01 Feb, 2024 (E)Measures of Dispersion
  35. 35Let the mean and the variance of 6 observation a , b , 68 , 44 , 48 , 60 be 55 and 194 , respectively if a b , then a + 3 b is31 Jan, 2024 (E)Measures of Dispersion
  36. 36Let M denote the median of the following frequency distribution. Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 3 9 10 8 6 Then 20 M is 30 Jan, 2024 (M)Median
  37. 37If the variance σ 2 of the data x i 0 1 5 6 10 12 17 f i 3 2 3 2 6 3 3 is k then the value of k is ______ {where . denotes the greatest inte30 Jan, 2024 (E)Measures of Dispersion
  38. 38If the mean and variance of the data 65 , 68 , 58 , 44 , 48 , 45 , 60 , α , β , 60 where α β are 56 and 66 . 2 respectively, then α 2 + β 2 29 Jan, 2024 (M)Measures of Dispersion
  39. 39If the mean and variance of five observations are 24 5 and 194 25 respectively and the mean of first four observations is 7 2 , then the var29 Jan, 2024 (E)Measures of Dispersion
  40. 40Let a 1 , a 2 , . . . , a 10 be 10 observations such that ∑ k = 1 10 a k = 50 and ∑ ∀ k j a k · a j = 1100 . Then the standard deviation of 27 Jan, 2024 (M)Measures of Dispersion
  41. 41The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation wa27 Jan, 2024 (E)Measures of Dispersion
  42. 42The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as15 Apr, 2023 (M)Measures of Dispersion
  43. 43Let the mean of the data x 1 3 5 7 9 Frequency f 4 24 28 8 be 5 . If m and 2 are respectively the mean deviation about the mean and the vari13 Apr, 2023 (M)Measures of Dispersion
  44. 44The 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 213 Apr, 2023 (E)Measures of Dispersion
  45. 45Let the positive numbers a 1 , a 2 , a 3 , a 4 and a 5 be in a G.P. Let their mean and variance be 31 10 and m n respectively, where m and n12 Apr, 2023 (M)Measures of Dispersion
  46. 46Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements11 Apr, 2023 (M)Measures of Dispersion
  47. 47Let the mean of 6 observations 1 , 2 , 4 , 5 , x and y be 5 and their variance be 10 . Then their mean deviation about the mean is equal to11 Apr, 2023 (E)Measures of Dispersion
  48. 48If the mean of the frequency distribution Class : 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency : 2 3 x 5 4 is 28 , then its variance is 10 Apr, 2023 (M)Measures of Dispersion
  49. 49Let be the mean and be the standard deviation of the distribution X i 0 1 2 3 4 5 f i k + 2 2 k k 2 - 1 k 2 - 1 k 2 + 1 k - 3 where f i = 6210 Apr, 2023 (E)Measures of Dispersion
  50. 50Let 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 3 x - 2 y is equal to _ 08 Apr, 2023 (M)Measures of Dispersion

Frequently Asked Questions

1.How many questions are available for Statistics?

This chapter includes 164 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Statistics chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Statistics an important chapter for JEE Main Mathematics?

Statistics has appeared in 25 of the 25 years of JEE Main papers covered here, with 164 questions across 160 papers - about one per paper it appears in.

4.What is the difficulty level of Statistics questions in JEE Main?

Of the 164 questions analysed for this chapter, 48% are easy, 48% moderate and 4% tough. 2023 had the most, with 21 questions.

5.Which topics in Statistics should I focus on?

These topics have carried the most weightage in Statistics:

  • Measures of Dispersion - 108 questions (66%)
  • Mean - 25 questions (15%)
  • Mean Square Deviation - 11 questions (7%)
  • Measures of Dispersion has produced the most tough questions (4).
6.Is Statistics's weightage in JEE Main going up or down?

Across all 160 papers analysed, Statistics has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.