NCERT Exemplar Class 10 Maths - Chapter 13 Statistics and Probability

1. In the formula \(\bar{x} = a + \dfrac{\sum f_i d_i}{\sum f_i}\), for finding the mean of grouped data \(d_i\)’s are deviations from \(a\) of

(A) lower limits of the classes
(B) upper limits of the classes
(C) mid points of the classes
(D) frequencies of the class marks

Correct Answer: (C)

2. While computing mean of grouped data, we assume that the frequencies are

(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

Correct Answer: (B)

3. If \(x_i\)’s are the mid points of the class intervals of grouped data, \(f_i\)’s are the corresponding frequencies and \(\bar{x}\) is the mean, then \(\sum (f_i x_i - \bar{x})\) is equal to

(A) 0 (B) –1 (C) 1 (D) 2

Correct Answer: (A)

4. In the formula \(\bar{x} = a + h \left( \dfrac{\sum f_i u_i}{\sum f_i} \right)\), for finding the mean of grouped frequency distribution, \(u_i =\)

(A) \(\dfrac{x_i + a}{h}\) (B) \(h(x_i - a)\) (C) \(\dfrac{x_i - a}{h}\) (D) \(\dfrac{a - x_i}{h}\)

Correct Answer: (C)

5. 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

(A) mean (B) median (C) mode (D) all the three above

Correct Answer: (B)

6. For the following distribution:
Class: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 10, 15, 12, 20, 9
the sum of lower limits of the median class and modal class is

(A) 15 (B) 25 (C) 30 (D) 35

Correct Answer: (B)

7. Consider the following frequency distribution:
Class: 0-5, 6-11, 12-17, 18-23, 24-29
Frequency: 13, 10, 15, 8, 11
The upper limit of the median class is

(A) 17 (B) 17.5 (C) 18 (D) 18.5

Correct Answer: (B)

8. For the following distribution:
Marks: Below 10, Below 20, Below 30, Below 40, Below 50, Below 60
Number of students: 3, 12, 27, 57, 75, 80
the modal class is

(A) 10-20 (B) 20-30 (C) 30-40 (D) 50-60

Correct Answer: (C)

9. Consider the data:
Class: 65-85, 85-105, 105-125, 125-145, 145-165, 165-185, 185-205
Frequency: 4, 5, 13, 20, 14, 7, 4
The difference of the upper limit of the median class and the lower limit of the modal class is

(A) 0 (B) 19 (C) 20 (D) 38

Correct Answer: (C)

10. The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:
Class: 13.8-14, 14-14.2, 14.2-14.4, 14.4-14.6, 14.6-14.8, 14.8-15
Frequency: 2, 4, 5, 71, 48, 20
The number of athletes who completed the race in less than 14.6 seconds is

(A) 11 (B) 71 (C) 82 (D) 130

Correct Answer: (C)

11. Consider the following distribution:
Marks obtained: More than or equal to 0, 10, 20, 30, 40, 50
Number of students: 63, 58, 55, 51, 48, 42
the frequency of the class 30-40 is

(A) 3 (B) 4 (C) 48 (D) 51

Correct Answer: (A)

12. If an event cannot occur, then its probability is

(A) 1 (B) \(\dfrac{3}{4}\) (C) \(\dfrac{1}{2}\) (D) 0

Correct Answer: (D)

13. Which of the following cannot be the probability of an event?

(A) \(\dfrac{1}{3}\) (B) 0.1 (C) 3% (D) \(\dfrac{17}{16}\)

Correct Answer: (D)

14. An event is very unlikely to happen. Its probability is closest to

(A) 0.0001 (B) 0.001 (C) 0.01 (D) 0.1

Correct Answer: (A)

15. If the probability of an event is \(p\), the probability of its complementary event will be

(A) \(p-1\) (B) \(p\) (C) \(1-p\) (D) \(1 - \dfrac{1}{p}\)

Correct Answer: (C)

16. The probability expressed as a percentage of a particular occurrence can never be

(A) less than 100 (B) less than 0 (C) greater than 1 (D) anything but a whole number

Correct Answer: (B)

17. If \(P(A)\) denotes the probability of an event A, then

(A) \(P(A) < 0\) (B) \(P(A) > 1\) (C) \(0 \leq P(A) \leq 1\) (D) \(-1 \leq P(A) \leq 1\)

Correct Answer: (C)

NCERT Exemplar Problems – Class 10 Mathematics

Chapter 13: Statistics and Probability