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

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

Answer

Answer: b


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

Answer

Answer: c


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

Answer

Answer: c


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

Answer

Answer: c


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

Answer

Answer: a


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

Answer

Answer: b


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

Answer

Answer: d


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

Answer

Answer: c


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

Answer

Answer: c


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

Answer

Answer: c


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

Answer

Answer: b


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

Answer

Answer: a


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

Answer

Answer: b


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

Answer

Answer: b


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

Answer

Answer: c


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

Answer/Explanation

Answer: c
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

Answer/Explanation

Answer: c
Explaination:
(c) Sum of 100 observations
= 100 × 49 = 4900
Correct sum
= 4900 – [40 + 20 + 50 ] + [60 + 70 + 80] = 5000
∴ Correct mean = \(\frac{5000}{100}\) = 50.


19. Choose the correct answer from the given four options : In the formula
MCQ Questions for Class 10 Maths Statistics with Answers 8
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

Answer/Explanation

Answer: c
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

Answer/Explanation

Answer: b
Explaination: (b) centred at the classmarks of the classes.


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
MCQ Questions for Class 10 Maths Statistics with Answers 9

Answer/Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 1


22. Mean of n numbers x1, x2, … xn is m. If xn is replaced by x, then new mean is
MCQ Questions for Class 10 Maths Statistics with Answers 10

Answer/Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 2
MCQ Questions for Class 10 Maths Statistics with Answers 3


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]
MCQ Questions for Class 10 Maths Statistics with Answers 11

Answer/Explanation

Answer: c
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

Answer/Explanation

Answer: b
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

Answer

Answer: c


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

Answer/Explanation

Answer: c
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]

Answer/Explanation

Answer: a
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

Answer/Explanation

Answer: b
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) \(\frac{3}{2}\)

Answer/Explanation

Answer: c
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.

Answer/Explanation

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


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

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 6


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

Answer/Explanation

Answer: b
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

Answer

Answer: b


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

Answer

Answer: b


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 ______ .

Answer/Explanation

Answer:
Explaination: 37.5


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

Answer/Explanation

Answer:
Explaination: (zero)


37. Find the class marks of classes 10 – 25 and 35 – 55.

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 4


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

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 5


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 ____ .

Answer/Explanation

Answer:
Explaination: 12


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

Answer/Explanation

Answer:
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

Answer/Explanation

Answer:
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 _____ .

Answer/Explanation

Answer:
Explaination: Median = \(\frac{66}{3}\) = 22.


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

Answer/Explanation

Answer:
Explaination: Median


44. In an arranged series of an even number of 2n terms the median is _______.

Answer/Explanation

Answer:
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.

Answer/Explanation

Answer:
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).

Answer/Explanation

Answer:
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
Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Statistics with Answers 7


48. There are ____ types of cumulative frequency curve.

Answer/Explanation

Answer:
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”?

Answer/Explanation

Answer:
Explaination: Median


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

Answer/Explanation

Answer:
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”?

Answer/Explanation

Answer:
Explaination: Median


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