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Mathematics - Statistics

Practise 77 NTA Abhyas (JEE Main) questions on Statistics. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Statistics has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 77 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The mean and standard deviation of 50 observations are 50 and 10 . Later on, it was decided to omit an observation that was incorrectly reco
  2. 2For two data sets, each with size 5 , the variances are given to be 3 and 4 and the corresponding means are given to be 2 and 4 , respective
  3. 3The mean square deviation of a set of observations x 1 , x 2 . . . . . . x n about a point m is defined as 1 n ∑ i = 1 n x i - m 2 . If the
  4. 4If x 1 , x 2 , x 3 , x 4 , x 5 . . . . . . . x n are n observations such that ∑ i = 1 n x i 2 = 400 and ∑ i = 1 n x i = 100 , then the possi
  5. 5The mean and variance of 7 observations are 7 and 22 respectively. If 5 of the observations are 2,4 , 10 , 12,14 , then the remaining 2 obse
  6. 6The mean deviation of the series a 2 , a 2 + d , a 2 + 2 d , . . . . . , a 2 + 2 n d from its median is
  7. 7For a sample size of 10 observations x 1 , x 2 , . . . x 10 , if i = 1 10 x i - 5 2 = 350 and i = 1 10 x i - 2 = 60 , then the variance of x
  8. 8The standard deviation of a distribution is 30. If each observation is increased by 5 , then the new standard deviation will be
  9. 9Let V 1 = variance of 13,16,19 . . . . . . . . . . 103 and V 2 = variance of 20,26,32 . . . . . . . . . . 200 . Then V 1 : V 2 is
  10. 10Let X n denote the mean of first n natural numbers, then the mean of X 1 , X 2 , … , X 100 is
  11. 11If x 1 , x 2 , x 3 . . . x 34 are numbers such that x i = x i + 1 = 150 , i 1,2 , 3,4 , . . . . 9 and x i + 1 - x i = - 2 , i 10,11 , . . .
  12. 12If the variance of the data 12 , 14 , 18 , 19 , 21 , 36 is , then the value of 3 is equal to
  13. 13If the variate of a distribution takes the values 1 2 , 2 2 , 3 2 , . . . n 2 with frequencies n , n - 1 , n - 2 , . . . 3,2 , 1 respectivel
  14. 14Let one observation equal to the mean is added to n observations. If the variance changes from 78 to 72 , then n is equal to
  15. 15If for a sample size of 10 , i = 1 10 x i - 5 2 = 350 and i = 1 10 x i - 6 =20 , then the variance is
  16. 16The mean of n observations is X ¯ . If the first observation is increased by 1 2 , second by 2 2 and so on, then the new mean is
  17. 17In an experiment with 9 observations on x , the following results are available ∑ x 2 = 360 and ∑ x = 34 . One observation that was 8 , was
  18. 18The mean of five numbers is 0 and their variance is 2 . If three of those numbers are - 1 , 1 and 2 , then the other two numbers are
  19. 19The mean of a data set comprising of 16 observations is 16 . If one of the observation valued 16 is deleted and three new observations value
  20. 20The mean and standard deviation of 10 observations x 1 , x 2 , x 3 . . . . . x 10 are x ¯ and σ respectively. Let 10 is added to x 1 , x 2 .
  21. 21A number equal to 4 times of the mean and a frequency equal to k is inserted in the data of n observations. If the new mean is 7 5 times the
  22. 22The mean of n items is x - . If the first item is increased by n , second by n - 1 and so on and last by 1, then the new mean is
  23. 23The average weight of students in a class of 32 students is 40 k g . If the weight of the teacher be included, the average rises by 1 3 k g
  24. 24All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 12 to the entire class. Which of the
  25. 25The mean and standard deviation of 100 observations were calculated as 40 and 5.1 , respectively by a student who took by mistake 50 instead
  26. 26If both the mean and the standard deviation of 50 observations x 1 , x 2 , … , x 50 are equal to 16 , then the mean of x 1 - 4 2 , x 2 - 4 2
  27. 27If the mean of a set of observations x 1 , x 2 , x 3 , . . . . , x n is x , then the mean of observations x i + 2 i , i = 1,2 , 3 , . . . .
  28. 28Let x 1 , x 2 , x 3 . . . . x k be k observations and w i = a x i + b for i = 1, 2 , 3 . . . . . k , where a and b are constants. If mean of
  29. 29The median of a set of 9 distinct observations is 20.5 . If each of the largest 4 observations of the set is increased by 4 , then the media
  30. 30If the observations 1 , 2 , 3 , … . , n occur with frequency n , n - 1 , n - 2 , . . , 1 respectively such that the mean of observations is
  31. 31The average of five consecutive odd numbers is 61. Then the difference between the highest and lowest numbers is
  32. 32Mean deviation of the series a 2 , a 2 + d , a 2 + 2 d , . . . . . . . . , a 2 + 2 n d from its mean is
  33. 33If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16 , then the value of m + n is
  34. 34The mean and variance of a data set comprising 15 observations are 15 and 5 respectively. If one of the observation 15 is deleted and two ne
  35. 35If the variance of the following data : 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 is K , then the value of K 11 is
  36. 36If the mean of 50 observations is 25 and their standard deviation is 4 and the sum of the squares of all the observations is λ , then λ 1000
  37. 37In ten observations, the mean of all 10 numbers is 15 , the mean of the first six observations is 16 and the mean of the last five observati
  38. 38Two data sets each of size 10 has the variance as 4 and k and the corresponding means as 2 and 4 respectively. If the variance of the combin
  39. 39If the variance of the first 50 odd natural numbers is V 1 and the variance of next 50 odd natural numbers is V 2 , then V 1 + V 2 is equal
  40. 40All the students of a class performed poorly in physics. The teacher decided to give grace marks of 15 to the entire class. Which of the fol
  41. 41Let x 1 , x 2 … , x n be n observations such that ∑ x i 2 = 300 and ∑ x i = 90 . Then a possible value of n among the following is
  42. 42The mean of five observations is 4 and their variance is 2.8 . If three of these observations are 2 , 2 and 5 , then the other two are
  43. 43The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2 , 4 , 10 , 12 and 14 , then the rem
  44. 44The ratio of the variance of first n positive integral multiples of 4 to the variance of first n positive odd numbers is
  45. 45A number equal to 2 times the mean and with a frequency equal to k is inserted in a data having n observations. If the new mean is 4 3 times
  46. 46The mean and variance of 5 observations are 6 and 6.8 respectively. If a number equal to mean is included in the set of observations and the
  47. 47If the mean and the variance of the numbers a , b , 8, 5 and 10 are 6 and 6 . 8 respectively, then the value of a 3 + b 3 is equal to
  48. 48The arithmetic mean of a set of 50 numbers is 38 . If two numbers of the set, namely 60 and 40 are discarded, the arithmetic mean of the rem
  49. 49If i = 1 5 x i - 6 = 5 and i = 1 5 x i - 6 2 = 25 , then the standard deviation of observations 3 x 1 + 2, 3 x 2 + 2, 3 x 3 + 2 , 3 x 4 + 2
  50. 50If the standard deviation of the numbers 2 , 4 , a and 10 is 3.5 , then which of the following is true?

Frequently Asked Questions

1.How many questions are available for Statistics?

This chapter includes 77 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Statistics questions in NTA Abhyas (JEE Main)?

Of the 77 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Statistics should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.