MATHEMATICS CLASS- 10
MCQ- CH-13(Statistics)
Class 10 Mathematics
Chapter 13: Statistics
50 Board-Level MCQs with Answers and Solutions
Q1. The arithmetic mean of 10, 15 and 20 is
(a) 12
(b) 15
(c) 18
(d) 20
Answer: (b) 15
Solution: Mean = (10 + 15 + 20)/3 = 15.
Q2. The median of 5, 7, 9, 11, 13 is
(a) 7
(b) 9
(c) 11
(d) 13
Answer: (b) 9
Q3. The mode of 2, 3, 4, 4, 4, 5, 6 is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Q4. Mean is also called
(a) Average
(b) Mode
(c) Median
(d) Frequency
Answer: (a) Average
Q5. The median divides the data into
(a) Three equal parts
(b) Four equal parts
(c) Two equal parts
(d) Five equal parts
Answer: (c)
Q6. The mode is the value which occurs
(a) Least frequently
(b) Most frequently
(c) Once only
(d) Twice only
Answer: (b)
Q7. The mean of first five natural numbers is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (b)
Solution: (1+2+3+4+5)/5 = 3.
Q8. The median of 4, 6, 8, 10 is
(a) 6
(b) 7
(c) 8
(d) 9
Answer: (b) 7
Q9. Which measure of central tendency is affected most by extreme values?
(a) Mean
(b) Median
(c) Mode
(d) None
Answer: (a)
Q10. If all observations are equal, then
(a) Mean = Median = Mode
(b) Mean > Median
(c) Mode > Mean
(d) Mean < Median
Answer: (a)
Q11. The class mark of class interval 10–20 is
(a) 10
(b) 15
(c) 20
(d) 25
Answer: (b)
Q12. The sum of frequencies is called
(a) Mean
(b) Median
(c) Total Frequency (N)
(d) Mode
Answer: (c)
Q13. The mean of 12, 14, 16, 18 is
(a) 14
(b) 15
(c) 16
(d) 17
Answer: (b)
Q14. If Mean = 20 and Number of observations = 5, then sum of observations is
(a) 25
(b) 50
(c) 100
(d) 200
Answer: (c)
Q15. Which measure is called positional average?
(a) Mean
(b) Median
(c) Mode
(d) Frequency
Answer: (b)
Q16. Empirical relation is
(a) Mean = Median + Mode
(b) Mode = Mean + Median
(c) Mode = 3 Median − 2 Mean
(d) Median = Mean + Mode
Answer: (c)
Q17. If Mean = 20 and Median = 22, then Mode is
(a) 24
(b) 26
(c) 22
(d) 18
Answer: (b)
Solution: Mode = 3×22 − 2×20 = 26.
Q18. If Mode = 30 and Mean = 20, then Median is
(a) 20
(b) 22
(c) 23.33
(d) 25
Answer: (c)
Q19. The median class is the class containing
(a) Mean
(b) N/2th observation
(c) Mode
(d) Highest frequency
Answer: (b)
Q20. Which of the following is not a measure of central tendency?
(a) Mean
(b) Median
(c) Mode
(d) Frequency
Answer: (d)
Q21. (CBSE PYQ) Mean of 8, 12, 16, 20, 24 is
(a) 14
(b) 16
(c) 18
(d) 20
Answer: (b)
Q22. Median of 3, 5, 7, 9, 11, 13, 15 is
(a) 7
(b) 8
(c) 9
(d) 10
Answer: (c)
Q23. Mode of 5, 5, 5, 7, 7, 8 is
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (a)
Q24. If mean of 10 observations is 15, total sum is
(a) 100
(b) 120
(c) 150
(d) 180
Answer: (c)
Q25. In grouped data, median formula contains
(a) l
(b) h
(c) cf
(d) All of these
Answer: (d)
Q26. (CBSE PYQ) If Mean = 18 and Median = 20, Mode is
(a) 22
(b) 24
(c) 26
(d) 28
Answer: (b)
Q27. The modal class is the class having
(a) Lowest frequency
(b) Highest frequency
(c) Zero frequency
(d) Equal frequency
Answer: (b)
Q28. Class mark of 30–40 is
(a) 30
(b) 35
(c) 40
(d) 45
Answer: (b)
Q29. The mean of 2, 4, 6, 8, 10 is
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (b)
Q30. If Mean = Median, then Mode is
(a) Equal to Mean
(b) Double Mean
(c) Half Mean
(d) Zero
Answer: (a)
Q31. Median of 11, 13, 15, 17, 19, 21 is
(a) 15
(b) 16
(c) 17
(d) 18
Answer: (b)
Q32. If Mode = 50 and Median = 40, Mean equals
(a) 30
(b) 35
(c) 40
(d) 45
Answer: (b)
Solution: 50 = 3×40 − 2Mean ⇒ Mean = 35.
Q33. Which graph is commonly used for cumulative frequency?
(a) Histogram
(b) Bar Graph
(c) Ogive
(d) Pie Chart
Answer: (c)
Q34. The cumulative frequency is obtained by
(a) Multiplying frequencies
(b) Dividing frequencies
(c) Successive addition of frequencies
(d) Subtracting frequencies
Answer: (c)
Q35. The median of grouped data is determined from
(a) Histogram
(b) Ogive
(c) Pie Chart
(d) Bar Graph
Answer: (b)
Q36. (CBSE PYQ) If Mean = 25 and Mode = 29, then Median is
(a) 26
(b) 27
(c) 28
(d) 29
Answer: (b)
Q37. Mean of 5 observations is 12. If one observation is increased by 5, new mean becomes
(a) 12.5
(b) 13
(c) 14
(d) 15
Answer: (b)
Q38. Which measure is easiest to calculate?
(a) Mean
(b) Median
(c) Mode
(d) None
Answer: (a)
Q39. The median of odd number of observations is
(a) Average of two middle terms
(b) Middle observation
(c) Highest observation
(d) Lowest observation
Answer: (b)
Q40. The mode may be found directly by
(a) Observation
(b) Formula only
(c) Graph only
(d) Equation only
Answer: (a)
Q41. Missing frequency problems are generally solved using
(a) Mean formula
(b) Median formula
(c) Mode formula
(d) All of these
Answer: (d)
Q42. (CBSE PYQ) Mean of 20 observations is 18. Sum of observations is
(a) 180
(b) 320
(c) 360
(d) 400
Answer: (c)
Q43. If Median = 25 and Mean = 20, Mode equals
(a) 30
(b) 35
(c) 25
(d) 20
Answer: (b)
Q44. The value occurring maximum number of times is called
(a) Mean
(b) Median
(c) Mode
(d) Range
Answer: (c)
Q45. Which measure is not affected much by extreme values?
(a) Mean
(b) Median
(c) Both Mean and Median
(d) None
Answer: (b)
Q46. If Mean = 40 and Median = 35, then Mode is
(a) 25
(b) 30
(c) 40
(d) 45
Answer: (a)
Q47. The empirical formula is applicable for
(a) Symmetrical distributions only
(b) Moderately skewed distributions
(c) All distributions exactly
(d) None
Answer: (b)
Q48. The frequency of a class represents
(a) Total observations
(b) Number of observations in that class
(c) Mean value
(d) Median value
Answer: (b)
Q49. The sum of all frequencies is denoted by
(a) f
(b) x
(c) N
(d) cf
Answer: (c)
Q50. Which statement is true?
(a) Mean is always equal to Mode.
(b) Median is always greater than Mean.
(c) Mode = 3 Median − 2 Mean is the empirical relation.
(d) Mode cannot be calculated.
Answer: (c) Mode = 3 Median − 2 Mean is the empirical relation.
Solution: This empirical formula is frequently used in CBSE Class 10 Statistics questions involving mean, median, mode and missing values.