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Mathematics - Statistics

Practise 236 NDA previous year questions on Statistics, compiled from papers spanning 2010 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 NDA tests.

Statistics has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 236 questions in all. 47% of them were easy, 53% moderate and 0% tough. Most of its questions came from 2011, with 25 questions that year. In the last three years (2024–2026) it had 25 questions across 5 papers, about 5 per paper.

The chapter's 8 topics are not weighted equally: Measures of Dispersion (71 questions, 30%), Mean (67 questions, 28%), and Statistics (54 questions, 23%) have been asked the most. Measures of Dispersion has also led over the last five years, with 22 questions.

  1. 1Let two lines of regression be and for some data. What is the value of correlation coefficient between and ?2026 (Phase 1)Measures of Dispersion
  2. 2If the mean of observations, namely is , then what is the value of ?2026 (Phase 1)Mean
  3. 3The standard deviation of observations is . If is multiplied to each of the observations, then what is the new standard deviation ?2026 (Phase 1)Measures of Dispersion
  4. 4If the random variable has mean and standard deviation , then what is the variance of the random variable ?2026 (Phase 1)Measures of Dispersion
  5. 5Passage: The frequency distribution of marks obtained by students in a certain subject is given below : Marks - - - - No. of students Questi2026 (Phase 1)Mean
  6. 6Passage: The frequency distribution of marks obtained by students in a certain subject is given below : Marks - - - - No. of students Questi2026 (Phase 1)Measures of Dispersion
  7. 7Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Heig2025 (Phase 1)Statistics
  8. 8Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Heig2025 (Phase 1)Median
  9. 9Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Heig2025 (Phase 1)Mode
  10. 10Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Heig2025 (Phase 1)Statistics
  11. 11Consider the following for the two (02) items that follow: The sum and the sum of squares of the observations corresponding to length (in cm2025 (Phase 1)Measures of Dispersion
  12. 12Consider the following for the two (02) items that follow: The sum and the sum of squares of the observations corresponding to length (in cm2025 (Phase 1)Measures of Dispersion
  13. 13The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithme2025 (Phase 1)Mean
  14. 14The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standa2025 (Phase 1)Measures of Dispersion
  15. 15What is the arithmetic mean of , , , , ?2025 (Phase 1)Mean
  16. 16The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation?2025 (Phase 2)Measures of Dispersion
  17. 17The frequency distribution of the marks obtained by students in a Science examination is given below: Marks 5–15 15–25 25–35 35–45 Number of2025 (Phase 2)Mean
  18. 18Consider the following statements: I. Mean and variance have the same unit of measurement. II. Mean deviation and standard deviation have th2025 (Phase 2)Mean
  19. 19From data and , the regression line of on is obtained as , then what is the value of ?2024 (Phase 1)Mean
  20. 20$ {array}{|c|c|c|c|c|c|} _i & 1 & 2 & 3 & & n \\ _i & 1 & 2^{-1} & 2^{-2} & & 2^{-(n-1)} \\ {array} What is the mean of the distribution?2024 (Phase 1)Mean
  21. 21The marks obtained by 10 students in a Statistics test are and 41. What is the mean deviation of the largest five observations?2024 (Phase 1)Measures of Dispersion
  22. 22The marks obtained by 10 students in a Statistics test are and 41. What is the variance of the largest five observations?2024 (Phase 1)Measures of Dispersion
  23. 23What is the mean deviation of the first 10 natural numbers?2024 (Phase 2)Measures of Dispersion
  24. 24Let . If M is the mean and is the standard deviation of , then what is the value of2024 (Phase 2)Measures of Dispersion
  25. 25The mean of the series is . If is replaced by , then what is the new mean?2024 (Phase 2)Mean
  26. 26The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11,16 and 20. What are the other2023 (Phase 1)Measures of Dispersion
  27. 27The central angles and (in degrees) of four sectors in a Pie Chart satisfy the relation . What is the value of ?2023 (Phase 1)Statistics
  28. 28The observations are outputs of 12 dices thrown simultaneously. If and are means of lowest 8 observations and highest 4 observations respect2023 (Phase 1)Mean
  29. 29The bivariate data set contains only two points and ( 3,2 ) What will be the line of regression of y on ?2023 (Phase 1)Statistics
  30. 30A die is thrown 10 times and obtained the following outputs: What will be the mode of data so obtained?2023 (Phase 1)Mode
  31. 31Consider the following frequency distribution: What is the value of median of the distribution?2023 (Phase 1)Median
  32. 32For data ; if M is the median of first 5 observations and is the median of last five observations then what is the value of ?2023 (Phase 1)Median
  33. 33Let represent mean, median and mode. If for some distribution , then what is equal to?2023 (Phase 1)Relation Between Mean, Median and Mode
  34. 34Let be the median, be the mean and be the mode of observations . Let takes minimum value, when is equal to2023 (Phase 1)Mean Square Deviation
  35. 35The sum of deviations of n numbers from 10 and 20 are and respectively. If , then what is the value of ?2023 (Phase 2)Measures of Dispersion
  36. 36If is the mean of 10 observations , then what is the value of ?2023 (Phase 2)Mean
  37. 37If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?2023 (Phase 2)Measures of Dispersion
  38. 38If is the coefficient of correlation between x and y , then what is the correlation coefficient between and2023 (Phase 2)Measures of Dispersion
  39. 39The frequency curve (assuming unimodal) corresponding to the data obtained in an experiment is skewed to the left. What conclusion can be dr2022 (Phase 1)Relation Between Mean, Median and Mode
  40. 40The variance of five positive observations is 3.6. If four of the observations are then what is the remaining observation?2022 (Phase 1)Measures of Dispersion
  41. 41What is the coefficient of mean deviation of , (taken from mean)?2022 (Phase 1)Measures of Dispersion
  42. 42The algebraic sum of the deviations of a set of values , measured from 100 is -20 and the algebriac sum of the deviations of the same set of2022 (Phase 1)Mean
  43. 43The algebraic sum of the deviations of a set of values , measured from 100 is -20 and the algebriac sum of the deviations of the same set of2022 (Phase 1)Mean
  44. 44The algebraic sum of the deviations of a set of values , measured from 100 is -20 and the algebriac sum of the deviations of the same set of2022 (Phase 1)Mean
  45. 45p$ ?2022 (Phase 1)Mean
  46. 46q$ ?2022 (Phase 1)Mean
  47. 47$ {array}{|c|c|c|c|c|c|} Class & 0-20 & 20-40 & 40-60 & 60-80 & 80-100 \\ Frequency & 17 & p+q & 32 & p-3 q & 19 \\ {array} The total freque2022 (Phase 1)Mean
  48. 48The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples was noted to be . Ass2022 (Phase 2)Statistics
  49. 49The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below: Which one of the following s2022 (Phase 2)Measures of Dispersion
  50. 50The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below: What is the coefficient of v2022 (Phase 2)Measures of Dispersion

Frequently Asked Questions

1.How many questions are available for Statistics?

This chapter includes 236 questions compiled from NDA papers spanning 2010 to 2026.

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

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

3.Is Statistics an important chapter for NDA Mathematics?

Statistics has appeared in 17 of the 17 years of NDA papers covered here, with 236 questions across 32 papers - about 7 per paper it appears in.

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

Of the 236 questions analysed for this chapter, 47% are easy, 53% moderate and 0% tough. 2011 had the most, with 25 questions.

5.Which topics in Statistics should I focus on?

These topics have carried the most weightage in Statistics:

  • Measures of Dispersion - 71 questions (30%)
  • Mean - 67 questions (28%)
  • Statistics - 54 questions (23%)
6.Is Statistics's weightage in NDA going up or down?

Across all 32 papers analysed, Statistics has averaged about 7.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 5.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.