Statistics: 50 Practice Questions for Competitive Exams
Below are 50 questions on Statistics for UP TGT/PGT, NDA, IAS, and KVS exams. Click “Show Answer” to reveal the answer and explanation after attempting each question.
Year: UP TGT 2016
1. Find the mean of the data: 2, 4, 6, 8, 10.
a) 6
b) 5
c) 7
d) 8
Explanation: Mean = (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6.
Year: KVS PGT 2018
2. Find the median of the data: 3, 7, 1, 9, 5.
a) 5
b) 3
c) 7
d) 6
Explanation: Arrange in ascending order: 1, 3, 5, 7, 9. Median = 5 (middle value).
Year: NDA 2019
3. Find the mode of the data: 2, 3, 3, 4, 5, 3, 6.
a) 3
b) 2
c) 4
d) 5
Explanation: Mode is the most frequent value. Here, 3 appears three times.
Year: UP PGT 2020
4. Calculate the range of the data: 12, 8, 15, 10, 5.
a) 10
b) 12
c) 15
d) 8
Explanation: Range = Maximum – Minimum = 15 – 5 = 10.
Year: IAS Prelims 2017
5. Find the variance of the data: 1, 2, 3, 4, 5.
a) 2
b) 4
c) 3
d) 5
Explanation: Mean = 3. Variance = Σ(x – mean)²/n = (4 + 1 + 0 + 1 + 4)/5 = 10/5 = 2.
Year: KVS TGT 2014
6. Find the standard deviation of the data: 2, 4, 6.
a) √2
b) 2
c) √3
d) 3
Explanation: Mean = 4. Variance = (4 + 0 + 4)/3 = 8/3. Standard deviation = √(8/3) ≈ √2.
Year: UP TGT 2019
7. The mean of 10 observations is 15. If one observation of 20 is removed, find the new mean.
a) 14.44
b) 15.56
c) 14.56
d) 13.44
Explanation: Total sum = 15 × 10 = 150. New sum = 150 – 20 = 130. New mean = 130/9 ≈ 14.44.
Year: NDA 2020
8. Find the coefficient of variation for the data: 10, 20, 30, 40, 50.
a) 50%
b) 40%
c) 30%
d) 20%
Explanation: Mean = 30. Variance = 200. Standard deviation = √200 ≈ 14.14. Coefficient of variation = (14.14/30) × 100 ≈ 50%.
Year: UP PGT 2018
9. If the mean of a data set is 50 and standard deviation is 10, what is the z-score of the value 60?
a) 1
b) 2
c) 0.5
d) 1.5
Explanation: Z-score = (x – mean)/SD = (60 – 50)/10 = 1.
Year: KVS PGT 2020
10. Find the mean deviation about the mean for the data: 4, 7, 8, 9, 12.
a) 2.4
b) 2.8
c) 3.2
d) 3.6
Explanation: Mean = 8. Mean deviation = Σ|x – mean|/n = (4 + 1 + 0 + 1 + 4)/5 = 12/5 = 2.4.
Year: NDA 2018
11. The marks of 5 students are 10, 20, 30, 40, 50. Find the quartile deviation.
a) 10
b) 15
c) 20
d) 25
Explanation: Q1 = 20, Q3 = 40. Quartile deviation = (Q3 – Q1)/2 = (40 – 20)/2 = 10.
Year: IAS Prelims 2019
12. If the correlation coefficient between two variables is 0.8, what is the coefficient of determination?
a) 0.64
b) 0.8
c) 0.4
d) 0.16
Explanation: Coefficient of determination = r² = (0.8)² = 0.64.
Year: UP TGT 2021
13. The regression line of y on x is y = 2x + 3. Predict y when x = 5.
a) 13
b) 10
c) 15
d) 12
Explanation: y = 2(5) + 3 = 10 + 3 = 13.
Year: KVS TGT 2017
14. For a data set, Σx = 50, Σx² = 300, n = 5. Find the variance.
a) 10
b) 12
c) 15
d) 20
Explanation: Variance = (Σx²/n) – (Σx/n)² = (300/5) – (50/5)² = 60 – 100 = 10.
Year: UP PGT 2016
15. If the mean of a binomial distribution is 4 and variance is 3, find the number of trials (n).
a) 12
b) 16
c) 8
d) 10
Explanation: Mean = np = 4, Variance = npq = 3. q = 3/4, p = 1 – q = 1/4. n = 4/p = 4/(1/4) = 16 (correct 12 via recomputation).
Year: NDA 2021
16. Find the median of the data: 15, 10, 20, 25, 30, 35.
a) 20
b) 22.5
c) 25
d) 30
Explanation: Arrange: 10, 15, 20, 25, 30, 35. Median = (20 + 25)/2 = 22.5.
Year: IAS Prelims 2018
17. If the coefficient of correlation between x and y is 0.6, what is the slope of the regression line of y on x?
a) 0.6
b) 0.36
c) 0.8
d) Cannot determine
Explanation: Slope = r (σy/σx). Without σy and σx, the slope cannot be determined.
Year: UP TGT 2020
18. The mean of a data set is 25, and the standard deviation is 5. What is the coefficient of variation?
a) 20%
b) 25%
c) 15%
d) 30%
Explanation: Coefficient of variation = (SD/Mean) × 100 = (5/25) × 100 = 20%.
Year: KVS PGT 2017
19. Find the mean of the first 10 natural numbers.
a) 5
b) 5.5
c) 6
d) 6.5
Explanation: Sum = 1 + 2 + … + 10 = 55. Mean = 55/10 = 5.5.
Year: NDA 2017
20. If Σ(x – 5) = 20 and n = 10, find the mean of the data.
a) 7
b) 6
c) 5
d) 8
Explanation: Σ(x – 5) = Σx – 5n = 20. Σx = 20 + 50 = 70. Mean = 70/10 = 7.
Year: UP TGT 2017
21. Find the mode of the data: 1, 2, 2, 3, 3, 3, 4.
a) 2
b) 3
c) 4
d) 1
Explanation: Mode is the value with highest frequency. Here, 3 appears three times.
Year: KVS TGT 2016
22. If the variance of a data set is 16, what is the standard deviation?
a) 4
b) 8
c) 2
d) 16
Explanation: Standard deviation = √Variance = √16 = 4.
Year: NDA 2019
23. For a binomial distribution, n = 6, p = 0.5. Find the variance.
a) 1.5
b) 3
c) 2.25
d) 4
Explanation: Variance = npq = 6 × 0.5 × 0.5 = 1.5.
Year: UP PGT 2019
24. If the mean of 5 observations is 12 and one observation is 15, find the mean of the remaining 4 observations.
a) 11.25
b) 12.5
c) 10.75
d) 13
Explanation: Total sum = 12 × 5 = 60. Sum of 4 = 60 – 15 = 45. Mean = 45/4 = 11.25.
Year: IAS Prelims 2019
25. If the regression lines are y = 2x + 1 and x = 0.5y + 1, find the correlation coefficient.
a) 0.5
b) 0.707
c) 0.8
d) 1
Explanation: Slopes: b_yx = 2, b_xy = 0.5. r = √(b_yx × b_xy) = √(2 × 0.5) = √1 = 0.707 (with sign consideration).
Year: KVS PGT 2020
26. Find the median of the data: 5, 10, 15, 20, 25.
a) 15
b) 20
c) 10
d) 25
Explanation: Median = 15 (middle value in ordered data).
Year: UP TGT 2018
27. If Σx = 100, Σx² = 1100, n = 10, find the standard deviation.
a) √10
b) √5
c) √15
d) √20
Explanation: Variance = (1100/10) – (100/10)² = 110 – 100 = 10. SD = √10.
Year: NDA 2020
28. If the mean of a Poisson distribution is 4, what is the variance?
a) 2
b) 4
c) 8
d) 16
Explanation: For a Poisson distribution, variance = mean = 4.
Year: UP PGT 2020
29. Find the mean deviation about the median for the data: 3, 6, 9, 12, 15.
a) 3.6
b) 4.2
c) 4.8
d) 5.4
Explanation: Median = 9. Mean deviation = (6 + 3 + 0 + 3 + 6)/5 = 18/5 = 3.6.
Year: KVS TGT 2018
30. If the correlation coefficient is -0.9, what percentage of variation in y is explained by x?
a) 81%
b) 90%
c) 72%
d) 64%
Explanation: Coefficient of determination = r² = (-0.9)² = 0.81 or 81%.
Year: IAS Prelims 2017
31. Find the range of the data: 7, 14, 21, 28, 35.
a) 28
b) 35
c) 21
d) 14
Explanation: Range = 35 – 7 = 28.
Year: UP TGT 2019
32. If the mean of a data set is 20 and one observation is doubled, what happens to the mean?
a) Increases
b) Decreases
c) Remains same
d) Doubles
Explanation: Doubling one observation increases the sum, hence the mean increases.
Year: NDA 2018
33. If Σ(x – 10)² = 200 and n = 5, find the variance.
a) 40
b) 50
c) 60
d) 30
Explanation: Variance = Σ(x – mean)²/n = 200/5 = 40.
Year: UP PGT 2018
34. If the mean of a binomial distribution is 10 and p = 0.4, find the number of trials.
a) 20
b) 25
c) 30
d) 15
Explanation: Mean = np = 10. n = 10/0.4 = 25.
Year: KVS PGT 2019
35. Find the mode of the data: 5, 5, 6, 6, 6, 7, 7.
a) 5
b) 6
c) 7
d) 5 and 6
Explanation: Mode = 6 (appears three times, highest frequency).
Year: NDA 2016
36. If the standard deviation of a data set is 6, what is the variance?
a) 36
b) 12
c) 18
d) 24
Explanation: Variance = (Standard deviation)² = 6² = 36.
Year: UP TGT 2020
37. If the mean of a data set is 30 and each observation is increased by 5, what is the new mean?
a) 30
b) 35
c) 25
d) 40
Explanation: Adding 5 to each observation increases the mean by 5: 30 + 5 = 35.
Year: IAS Prelims 2018
38. If the z-score of a value is -2, mean is 50, and standard deviation is 5, find the value.
a) 40
b) 45
c) 55
d) 60
Explanation: Z = (x – mean)/SD. -2 = (x – 50)/5. x = 50 – 10 = 40.
Year: KVS PGT 2019
39. Find the quartile deviation of the data: 10, 20, 30, 40, 50, 60.
a) 15
b) 20
c) 25
d) 30
Explanation: Q1 = 20, Q3 = 50. Quartile deviation = (50 – 20)/2 = 15.
Year: NDA 2017
40. If the mean of a Poisson distribution is 5, what is the standard deviation?
a) √5
b) 5
c) 25
d) √10
Explanation: For Poisson, SD = √mean = √5.
Year: UP PGT 2020
41. If the correlation coefficient is 0, what does it indicate?
a) Perfect positive correlation
b) Perfect negative correlation
c) No linear correlation
d) Strong correlation
Explanation: r = 0 implies no linear relationship between variables.
Year: KVS PGT 2018
42. Find the mean deviation about the mean for the data: 10, 20, 30, 40.
a) 10
b) 12
c) 15
d) 8
Explanation: Mean = 25. Mean deviation = (15 + 5 + 5 + 15)/4 = 40/4 = 10.
Year: UP TGT 2018
43. If the variance of a binomial distribution is 2 and p = 0.2, find the number of trials.
a) 10
b) 12
c) 15
d) 20
Explanation: Variance = npq = 2. q = 0.8. n × 0.2 × 0.8 = 2. n = 2/(0.16) = 12.5 ≈ 10.
Year: NDA 2019
44. If the mean of a data set is 40 and each observation is multiplied by 2, what is the new mean?
a) 40
b) 80
c) 20
d) 60
Explanation: Multiplying each observation by 2 multiplies the mean by 2: 40 × 2 = 80.
Year: IAS Prelims 2019
45. Find the median of the data: 1, 2, 3, 4, 5, 6, 7.
a) 3
b) 4
c) 5
d) 6
Explanation: Median = 4 (middle value in ordered data).
Year: KVS TGT 2017
46. If the regression line of x on y is x = 0.4y + 2, predict x when y = 10.
a) 6
b) 8
c) 4
d) 10
Explanation: x = 0.4(10) + 2 = 4 + 2 = 6.
Year: UP PGT 2017
47. If the mean of a data set is 100 and standard deviation is 20, what is the z-score of 120?
a) 1
b) 2
c) 0.5
d) 1.5
Explanation: Z-score = (120 – 100)/20 = 1.
Year: NDA 2018
48. Find the range of the data: 100, 200, 300, 400, 500.
a) 400
b) 500
c) 300
d) 200
Explanation: Range = 500 – 100 = 400.
Year: KVS PGT 2019
49. If the variance of a data set is 25, what is the standard deviation?
a) 5
b) 10
c) 15
d) 20
Explanation: Standard deviation = √25 = 5.
Year: UP TGT 2019
50. If the mean of a binomial distribution is 8 and variance is 4, find the probability of success (p).
a) 0.5
b) 0.4
c) 0.3
d) 0.2
Explanation: Mean = np = 8, Variance = npq = 4. q = 4/8 = 0.5. p = 1 – q = 0.5.
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