NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability
Exercise 13.1

Choose the correct answer from the given four options:

Question.  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 (class marks) of the classes

(D)

frequencies of the class marks

Open

Question.  2

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

(A)

evenly distributed over all the classes

(B)

centred at the class marks of the classes

(C)

centred at the upper limits of the classes

(D)

centred at the lower limits of the classes

Open

Question.  3

If \(x_i\) are the class marks and \(f_i\) the corresponding frequencies with mean \(\bar{x}\), then \(\sum f_i(x_i-\bar{x})\) equals

(A)

0

(B)

-1

(C)

1

(D)

2

Open

Question.  4

In the formula \(\bar{x}=a+h\,\dfrac{\sum f_i u_i}{\sum f_i}\) for mean of grouped data, \(u_i=\)

(A)

\(\dfrac{x_i+a}{h}\)

(B)

\(h(x_i-a)\)

(C)

\(\dfrac{x_i-a}{h}\)

(D)

\(\dfrac{a-x_i}{h}\)

Open

Question.  5

The abscissa of the intersection point of the less-than and more-than cumulative frequency curves of a grouped data gives its

(A)

mean

(B)

median

(C)

mode

(D)

all the three above

Open

Question.  6

For the following distribution:

Class0–55–1010–1515–2020–25
Frequency101512209

the sum of lower limits of the median class and modal class is

(A)

15

(B)

25

(C)

30

(D)

35

Open

Question.  7

Consider the distribution:

Class0–56–1112–1718–2324–29
Frequency131015811

The upper limit of the median class is

(A)

17

(B)

17.5

(C)

18

(D)

18.5

Open

Question.  8

For the following distribution:

MarksBelow 10Below 20Below 30Below 40Below 50Below 60
No. of students31227577580

The modal class is

(A)

10–20

(B)

20–30

(C)

30–40

(D)

50–60

Open

Question.  9

Consider the data:

Class65–8585–105105–125125–145145–165165–185185–205
Frequency4513201474

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

Open

Question.  10

Times (s) taken by 150 athletes in a 110 m hurdle race:

Class13.8–1414–14.214.2–14.414.4–14.614.6–14.814.8–15
Frequency245714820

The number who finished in less than 14.6 s is

(A)

11

(B)

71

(C)

82

(D)

130

Open

Question.  11

Consider:

Marks obtained≥0≥10≥20≥30≥40≥50
No. of students635855514842

The frequency of the class 30–40 is

(A)

3

(B)

4

(C)

48

(D)

51

Open

Question.  12

If an event cannot occur, its probability is

(A)

1

(B)

\(\dfrac{3}{4}\)

(C)

\(\dfrac{1}{2}\)

(D)

0

Open

Question.  13

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

(A)

\(\dfrac{1}{3}\)

(B)

0.1

(C)

3%

(D)

\(\dfrac{17}{16}\)

Open

Question.  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

Open

Question.  15

If the probability of an event is \(p\), the probability of its complementary event is

(A)

\(p-1\)

(B)

\(p\)

(C)

\(1-p\)

(D)

\(1-\dfrac{1}{p}\)

Open

Question.  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

Open

Question.  17

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

(A)

\(P(A)<0\)

(B)

\(P(A)>1\)

(C)

\(0\le P(A)\le 1\)

(D)

\(-1\le P(A)\le 1\)

Open

Question.  18

A card is selected from a deck of 52 cards. The probability that it is a red face card is

(A)

\(\dfrac{3}{26}\)

(B)

\(\dfrac{3}{13}\)

(C)

\(\dfrac{2}{13}\)

(D)

\(\dfrac{1}{2}\)

Open

Question.  19

The probability that a non-leap year selected at random will contain 53 Sundays is

(A)

\(\dfrac{1}{7}\)

(B)

\(\dfrac{2}{7}\)

(C)

\(\dfrac{3}{7}\)

(D)

\(\dfrac{5}{7}\)

Open

Question.  20

When a die is thrown, the probability of getting an odd number less than 3 is

(A)

\(\dfrac{1}{6}\)

(B)

\(\dfrac{1}{3}\)

(C)

\(\dfrac{1}{2}\)

(D)

0

Open

Question.  21

A card is drawn from a deck of 52 cards. Event \(E\): “card is not an ace of hearts”. The number of outcomes favourable to \(E\) is

(A)

4

(B)

13

(C)

48

(D)

51

Open

Question.  22

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is

(A)

7

(B)

14

(C)

21

(D)

28

Open

Question.  23

A girl finds the probability of winning the first prize in a lottery to be 0.08. If 6000 tickets are sold, how many tickets has she bought?

(A)

40

(B)

240

(C)

480

(D)

750

Open

Question.  24

One ticket is drawn at random from a bag of tickets numbered 1 to 40. The probability that the selected ticket is a multiple of 5 is

(A)

\(\dfrac{1}{5}\)

(B)

\(\dfrac{3}{5}\)

(C)

\(\dfrac{4}{5}\)

(D)

\(\dfrac{1}{3}\)

Open

Question.  25

Someone is asked to take a number from 1 to 100. The probability that it is a prime is

(A)

\(\dfrac{1}{5}\)

(B)

\(\dfrac{6}{25}\)

(C)

\(\dfrac{1}{4}\)

(D)

\(\dfrac{13}{50}\)

Open

Question.  26

A class has 23 students: 4 from house A, 8 from B, 5 from C, 2 from D and the rest from E. One student is selected at random to be the monitor. The probability that the selected student is not from A, B and C is

(A)

\(\dfrac{4}{23}\)

(B)

\(\dfrac{6}{23}\)

(C)

\(\dfrac{8}{23}\)

(D)

\(\dfrac{17}{23}\)

Open

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 13: Statistics and Probability – Exercise 13.1 | Detailed Answers