# MCQ Questions for Class 10 Maths Statistics with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 14 Statistics Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Statistics MCQs with Answers to know their preparation level.

## Class 10 Maths MCQs Chapter 14 Statistics

MCQ on Statistics Class 10 Question 1. One of the methods for determining mode is
(a) Mode = 2 Median -3 Mean
(b) Mode = 3 Median – 2 Mean
(c) Mode = 2 Mean – 3 Median
(d) Mode = 3 Mean – 2 Median

Statistics Class 10 MCQ with Answer: b

2. Mode is the
(a) middle most frequent value
(b) least frequent value
(c) maximum frequent value
(d) none of these

3. The algebraic sum of the deviations of a frequency distribution from its mean is always,
(a) greater than zero
(b) less than zero
(c) zero
(d) a non-zero number

MCQ Questions for Class 10 Maths Statistics Question 4. While computing mean of grouped data, we assume that the frequencies are
(a) centred at the upper limits of the classes
(b) centred at the lower limits of the classes
(c) centred at the classmarks of the classes
(d) evenly distributed over all the classes
5. Construction of a cumulative frequency table is useful in determining the
(a) mean
(b) median
(c) mode
(d) none of these

6. Which of the following can not be determined graphically?
(a) Mean
(b) Median
(c) Mode
(d) None of these

Statistics MCQ Class 10 Question 7. The absccissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its
(a) Mean
(b) Median
(c) Mode
(d) None of these

8. For the following distribution

 C.I. 0-10 10-20 20-30 30-40 40-50 f 20 30 24 40 18

the sum of lower limits of the modal class and the median class is
(a) 20
(b) 30
(c) 40
(d) 50

9. For the following distribution

 C.I. 0-5 6-11 12-17 18-23 24-29 f 26 20 30 16 22

the upper limit of the median class is
(a) 18.5
(b) 18
(c) 17.5
(d) 17

MCQ of Statistics Class 10 Question 10. For the following distribution

 Marks No. of students Less than 20 4 Less than 40 12 Less than 60 25 Less than 80 56 Less than 100 74 Less than 120 80

the modal class is
(a) 20 – 40
(b) 40 – 60
(c) 60 – 80
(d) 80 -100

11. For the following distribution

 Monthly Expenditure (?) No. of families Expenditure les than ? 10,000 15 Expenditure les than ? 13,000 31 Expenditure les than ? 16,000 50 Expenditure les than ? 19,000 67 Expenditure les than ?22,000 85 Expenditure les than ?25,000 100

The number of families having expenditure range (in ?) 16,000 – 19,000 is
(a) 15
(b) 16
(c) 17
(d) 19

12. In the given data:

 C.I. f 65-85 4 85 – 105 5 105 – 125 13 125 – 145 20 145 – 165 14 165 – 185 7 185 – 205 4

the difference of the upper limit of the median class and the lower limit of the modal class is
(a) 38
(b) 20
(c) 19
(d) 0

Statistics Class 10 MCQ Question 13. For the following distribution

 Cl 0-5 5-10 10-15 15-20 20-25 f 10 15 12 20 9

the difference of the upper limit of the median class and the lower limit of the modal class is
(a) 0
(b) 5
(c) 10
(d) -5

14. For the following distribution

 Marks 0-10 10-20 20-30 30-40 40-50 No. of students 3 9 13 10 5

the number of students who got marks less than 30 is
(a) 13
(b) 25
(c) 10
(d) 12

15. For the following distribution

 Marks obtained No. of students More than or equal to 0 63 More than or equal to 10 58 More than or equal to 20 55 More than or equal to 30 51 More than or equal to 40 48 More than or equal to 50 42

the frequency of the class 20-30 is
(a) 35
(b) 4
(c) 48
(d) 51

Class 10 Maths MCQ Questions with Answer: b

MCQ Questions for Class 10 Maths with Answers Question 16. The times, in seconds, taken by 150 atheletes to run a 100 m hurdle race are tabulated below:

 C.I. f 13.8-14 3 14 – 14.2 4 14.2 – 14.4 6 14.4 – 14.6 69 14.6 – 14.8 48 14.8-15 20

The number of atheletes who completed the race in less than 14.6 seconds is
(a) 13
(b) 69
(c) 82
(d) 130

17. di is the deviation of xi from assumed mean a. If mean = $$x+\frac{\sum f_{i} d_{i}}{\sum f_{i}}$$, then x is
(a) class size ‘
(b) number of observations
(c) assumed mean
(d) none of these

Explaination:
(c) ∵ Mean = assumed mean + $$\frac{\sum f_{i} d_{i}}{\sum f_{i}}$$
∴ x = assumed mean.

18. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is
(a) 48
(b) 49
(c) 50
(d) 60

Maths MCQ for Class 10 CBSE with Answer: cExplaination:
(c) Sum of 100 observations
= 100 × 49 = 4900
Correct sum
= 4900 – [40 + 20 + 50 ] + [60 + 70 + 80] = 5000
∴ Correct mean = $$\frac{5000}{100}$$ = 50.

MCQ on Statistics Class 9 Question 19. Choose the correct answer from the given four options : In the formula

for finding the mean of grouped data d1 s are deviation from a of [NCERT Exemplar Problems]
(a) lower limits of the classes
(b) upper limits of the classes
(c) mid points of the classes
(d) frequencies of the class marks

Explaination: (c) mid-points of the classes.

20. While computing mean of grouped data, we assume that the frequencies are [NCERT Exemplar Problems]
(a) evenly distributed over all the classes
(b) centred at the classmarks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classes

MCQ for Class 10 Maths with Answer: bExplaination: (b) centred at the classmarks of the classes.

CBSE Class 10 Maths MCQ Pdf Question 21. A car travels from city A to city B, 120 km apart at an average speed of 50 km/h. It then makes a return trip at an average speed of 60 km/h. It covers another 120 km distance at an average speed of 40 km/h. The average speed over the entire 360 km will be

Explaination:

22. Mean of n numbers x1, x2, … xn is m. If xn is replaced by x, then new mean is

Explaination:

Statistics MCQ Question 23. In the formula $$\bar{x}=a+h\left(\frac{\sum f_{i} u_{i}}{\sum f_{i}}\right)$$ finding the mean of grouped frequency distribution, ui = [NCERT Exemplar Problems]

Explaination: $$\frac{x_{i}-a}{h}$$

24. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its [NCERT Exemplar Problems]
(a) mean
(b) median
(c) mode
(d) all the three above

Explaination: median

25. For the following distribution:

 Marks Number of Students Below 10 3 Below 20 12 Below 30 27 Below 40 57 Below 50 75 Below 60 80

the modal class is
(a) 10 – 20
(b) 20 – 30
(c) 30 – 40
(d) 50 – 60

26. The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below:

 Class Frequency 13.8 – 14.0 2 14.0 – 14.2 4 14.2 – 14.4 5 14.4 – 14.6 71 14.6 – 14.8 48 14.8 – 15.0 20

The number of atheletes who completed the race in less then 14.6 seconds is: [NCERT Exemplar Problems]
(a) 11
(b) 71
(c) 82
(d) 130

Explaination: (c) 82

27. Mode is the value of the variable which has:
(a) maximum frequency
(b) minimum frequency
(c) mean frequency
(d) middle most frequency [CBSE 2012]

Explaination: (a) maximum frequency.

28. Mode and mean of a data are 12k and 15A. Median of the data is
(a) 12k
(b) 14k
(c) 15k
(d) 16k

Explaination:
(b) ∵ Mode = 3 median – 2 mean
⇒ 12k = 3 median – 2 × 15k
⇒ 42k = 3 median
⇒ Median = 14k.

29. If mean = (3 median – mode) . k, then the value of k is
(a) 1
(b) 2
(C) $$\frac{1}{2}$$
(d) $$\frac{3}{2}$$

Explaination:
(c) ∵ Mode = 3 median – 2 mean
⇒ 2 mean = 3 median – mode
⇒ mean = $$\frac{1}{2}$$ (3 median – mode)
⇒ k= $$\frac{1}{2}$$

30. The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
(a) is increased by 2
(b) is decreased by 2
(c) is two times of the original number
(d) Remains the same as that of the original set.

Explaination:
(d) No. of observations = 9
∴ median = 5th observation
∵ The largest four observations are increased
∴ 5th observation remains unchanged.

Maths Multiple Choice Questions with Answers for Class 10 Question 31. The median from the table is

 Value Frequency 7 2 8 1 9 4 10 5 11 6 12 1 13 3

(a) 11
(b) 10
(c) 12
(d) 11.5

Explaination:

32. The relationship between mean, median and mode for a moderately skewed distribution is
(a) mode = median – 2 mean
(b) mode = 3 median – 2 mean
(c) mode = 2 median – 3 mean
(d) mode = median – mean

Explaination: (b) Mode = 3 median – 2 mean

33. The abscissa of the point of intersection
of both types (less than & more than) of cumulative frequency curves help in finding
(a) mean
(b) median
(c) mode
(d) None of these

34. Cumulative frequency curve is also called
(a) histogram
(b) ogive
(c) bar graph
(d) median

35. The A.M. of a set of 50 numbers is 38. If two numbers of the set namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is ______ .

Explaination: 37.5

36. If x is the mean of a distribution, then Σfi(xi – x) is eclual t0 _____ .

Explaination: (zero)

Maths MCQ for Class 10 CBSE with Answers Pdf Question 37. Find the class marks of classes 10 – 25 and 35 – 55.

Explaination:

38. If Σfi = 11, Σfixi = 2p + 52 and the mean of any distribution is 6, find the value of p.

Explaination:

39. A set of numbers consists of four 5’s, six 7’s, ten 9’s, eleven 12’s, three 13’s, two 14’s. The mode of this set of numbers is ____ .

Explaination: 12

40. The mode of the numbers 2, 3, 4, 4. 3, 5, 3, 6 is ______ .

Explaination: 3

41. Find the value of x, if the mode of the following data is 25.
15, 20, 25, 18, 14, 15, 25, 15, 18, 16, 20. 25, 20, x, 18

Explaination:

 Observations Tally Marks f 14 1 1 15 III 3 16 1 1 18 III 3 20 III 3 25 III 3

Observations 15,18,20, and 25 all have the same frequency i.e., 3. For 25 be the mode of the data it should have the maximum frequency.
∴ 25 should repeat itself at least once more i.e., x should be 25.

42. If the mode of a data is 18 and the mean is 24. then median is _____ .

Explaination: Median = $$\frac{66}{3}$$ = 22.

43. Construction of cumulative frequency table is useful in determining the

Explaination: Median

Statistics Questions And Answers for Class 10 Question 44. In an arranged series of an even number of 2n terms the median is _______.

Explaination: mean of nth term and (n + 1)th term

45.

 x f c.f. 1 8 8 2 10 18 3 11 29 4 16 45 5 20 65 6 25 90 7 15 105 8 9 114 9 6 120

Find the median distribution.

Explaination:
n = 120
⇒ $$\frac{n}{2}$$ = 60
∴ Median is average of 60th and 61st observation
⇒ Median =$$\frac{5+5}{2}$$ = 5

46.

 Marks Number of students 0 and above 80 10 and above 77 20 and above 72 30 and above 65 40 and above 55 50 and above 43 60 and above 28 70 and above 16 80 and above 10 90 and above 8 100 and above 0

Write the proper data (marks) and frequency (Number of students).

Explaination:

 Marks Frequency 0 – 10 3 10 – 20 5 20 – 30 7 30 – 40 10 40 – 50 12 50 – 60 15 60 – 70 12 70 – 80 6 80 – 90 2 90 – 100 8

47. Find the median class of the following data:

 Marks obtained Frequency 0-10 8 10-20 10 20-30 12 30-40 22 40-50 30 50-60 18

Explaination:

48. There are ____ types of cumulative frequency curve.

Explaination: two

49. Which measure of central tendency is given by the x-coordinate of the point of intersection of the “more than ogive” and “less than ogive”?

Explaination: Median

50. In drawing ogive, cumulative frequencies are marked on _____ axis.

Explaination: y

51. Which measure of central tendency is given by the x-coordinate of the point of intersection of “more than ogive”.and “less than ogive”?

Explaination: Median

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