SSC CGL Tier 2 – Paper III: Statistics (50 Questions)

1. Mean of the numbers 5, 8, 10, 12, 15 is:
   A) 10
   B) 11
   C) 12
   D) 13
2. Median of 2, 5, 9, 12, 15, 18 is:
   A) 10.5
   B) 11
   C) 12
   D) 11.5
3. Mode of 4, 4, 5, 6, 6, 6, 7 is:
   A) 4
   B) 6
   C) 5
   D) 7
4. If variance of data 2, 4, 6, 8 is 5, the standard deviation is:
   A) √5
   B) 5
   C) 2.5
   D) 10
5. Coefficient of variation is defined as:
   A) Mean ÷ SD × 100
   B) SD ÷ Mean × 100
   C) Variance ÷ Mean × 100
   D) Mean ÷ Variance × 100
6. If sum of squares of deviations of 5 observations is 20, variance is:
   A) 4
   B) 5
   C) 6
   D) 2
7. Quartiles divide the data into:
   A) 2 equal parts
   B) 3 equal parts
   C) 4 equal parts
   D) 5 equal parts
8. Range of data 5, 7, 8, 10, 12 is:
   A) 5
   B) 6
   C) 7
   D) 8
9. Probability of getting a head in a single coin toss is:
   A) 1/2
   B) 1/3
   C) 1/4
   D) 2/3
10. If 3 coins are tossed, probability of exactly 2 heads is:
    A) 1/8
    B) 3/8
    C) 1/4
    D) 1/2
11. Sum of deviations from mean is always:
    A) Zero
    B) Positive
    C) Negative
    D) 1
12. Correlation coefficient r satisfies:
    A) -1 ≤ r ≤ 1
    B) 0 ≤ r ≤ 1
    C) -∞ ≤ r ≤ ∞
    D) 0 ≤ r ≤ ∞
13. Two events A and B are independent if:
    A) P(A∩B) = P(A) + P(B)
    B) P(A∩B) = P(A)P(B)
    C) P(A∪B) = P(A) + P(B)
    D) P(A∪B) = P(A)P(B)
14. A random variable X takes values 1, 2, 3 with probabilities 1/4, 1/2, 1/4. Its expected value E(X) = ?
    A) 2
    B) 3
    C) 1.5
    D) 2.5
15. A frequency distribution with unequal class intervals is called:
    A) Simple frequency distribution
    B) Grouped frequency distribution
    C) Relative frequency distribution
    D) Cumulative frequency distribution
16. The sum of all probabilities of a discrete probability distribution is:
    A) 0
    B) 1
    C) Greater than 1
    D) Less than 1
17. If P(A) = 0.3, P(B) = 0.5, and P(A∩B) = 0.15, P(A∪B) = ?
    A) 0.65
    B) 0.7
    C) 0.75
    D) 0.8
18. Standard deviation is the square root of:
    A) Mean
    B) Variance
    C) Coefficient of variation
    D) Range
19. If X and Y are independent, Cov(X, Y) = ?
    A) 1
    B) 0
    C) -1
    D) Undefined
20. Skewness measures:
    A) Central tendency
    B) Dispersion
    C) Symmetry of data
    D) Probability
21. For a normal distribution, mean = ?
    A) Median
    B) Mode
    C) Both A and B
    D) None
22. If two events cannot occur simultaneously, they are called:
    A) Mutually exclusive
    B) Independent
    C) Dependent
    D) Complementary
23. Cumulative frequency at median class = ? (definition)
    A) Half of total frequency
    B) Total frequency
    C) Twice total frequency
    D) One-fourth total frequency
24. If data: 2, 4, 6, 8, 10, variance = ?
    A) 8
    B) 6.8
    C) 6.67
    D) 5
25. Chebyshev’s theorem is applicable to:
    A) Only normal distribution
    B) Any distribution
    C) Only uniform distribution
    D) Only skewed distribution
26. Binomial distribution is:
    A) Discrete
    B) Continuous
    C) Both A and B
    D) None
27. Mean deviation from median is always:
    A) Less than mean deviation from mean
    B) Equal to mean deviation from mean
    C) Greater than mean deviation from mean
    D) Zero
28. If probability of success = 0.7, probability of failure = ?
    A) 0.3
    B) 0.7
    C) 1
    D) 0.5
29. The median of 2, 7, 4, 9, 12, 5 arranged in order:
    A) 5
    B) 7
    C) 6
    D) 4
30. Mean of 10 numbers is 12. If one number 18 is removed, new mean = ?
    A) 11
    B) 11.2
    C) 11.5
    D) 12
31. Probability of drawing an ace from a deck of 52 cards = ?
    A) 1/13
    B) 1/4
    C) 1/52
    D) 4/52
32. A histogram represents:
    A) Frequency distribution
    B) Probability distribution
    C) Cumulative frequency
    D) Mean and median
33. If variance = 0, data is:
    A) Constant
    B) Increasing
    C) Decreasing
    D) Random
34. The coefficient of skewness of a symmetric distribution is:
    A) 1
    B) 0
    C) -1
    D) Undefined
35. Cumulative frequency less than type gives:
    A) Less than distribution
    B) More than distribution
    C) Exact distribution
    D) Median
36. Poisson distribution is suitable for:
    A) Continuous data
    B) Discrete data
    C) Both
    D) None
37. The sum of deviations of x from mean is:
    A) Zero
    B) Positive
    C) Negative
    D) Equal to sum of squares
38. If mean = 10, SD = 2, CV = ?
    A) 20%
    B) 25%
    C) 15%
    D) 12%
39. Median of data 3, 7, 5, 8, 9 arranged:
    A) 6
    B) 7
    C) 5
    D) 8
40. Standard deviation of 4, 4, 4, 4 is:
    A) 4
    B) 0
    C) 1
    D) 2
41. Karl Pearson’s coefficient of skewness uses:
    A) Mean, median, SD
    B) Median, mode, variance
    C) Mean, mode, range
    D) Only median
42. Correlation coefficient r = -1 indicates:
    A) Perfect positive correlation
    B) Perfect negative correlation
    C) No correlation
    D) None
43. A cumulative frequency curve is called:
    A) Ogive
    B) Histogram
    C) Polygon
    D) Pie chart
44. Probability of getting sum 7 on two dice = ?
    A) 1/6
    B) 1/12
    C) 1/8
    D) 1/5
45. Standard deviation of 2, 2, 2, 2, 2 = ?
    A) 0
    B) 1
    C) 2
    D) 5
46. The range of 3, 7, 10, 15, 20 = ?
    A) 17
    B) 15
    C) 20
    D) 10
47. If mean of 5 numbers = 10, sum = ?
    A) 50
    B) 40
    C) 55
    D) 45
48. Coefficient of variation formula:
    A) SD ÷ Mean × 100
    B) Mean ÷ SD × 100
    C) Variance ÷ Mean × 100
    D) Range ÷ SD × 100
49. A data set 5, 10, 15, 20, 25, median = ?
    A) 15
    B) 14
    C) 16
    D) 12
50. Probability of drawing king from a deck of 52 cards = ?
    A) 1/13
    B) 1/52
    C) 4/52
    D) 1/4