class 10 maths Statistics questions with solutions

Q 1 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

Numbers announced Number of times

0-15 8

15-30 9

30-45 10

45-60 12

60-75 9

Based on the above information, answer the following:

(i) Write the median class.

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(30-45)

Numbers announced	Number of times	cf
0-15	8	8
15-30	9	17
30-45	10	27
45-60	12	39
60-75	9	48

Here, n = 48,

then n/2 = 48/2 = 24

$∴$ Median class : 30 – 45

Q 2 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

Numbers announced Number of times

0-15 8

15-30 9

30-45 10

45-60 12

60-75 9

Based on the above information, answer the following:

(ii) When first ball was picked up, what was the probability of calling out an even number?

0%

(37/75)

The number of even numbers between 1 to 75 is 37, [i.e., (75 – 1) ÷ 2 = 37]

Prob.(calling out an even number) = 37/75

Q 3 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

Numbers announced Number of times

0-15 8

15-30 9

30-45 10

45-60 12

60-75 9

Based on the above information, answer the following:

(iii) Find median of the given data.

0%

(40.5)

$l = 30, c f = 17, f = 10, h = 15$

$Median = l + (\frac{\frac{n}{2} - c f}{f}) \times h$

$\Rightarrow Median = 30 + (\frac{24 - 17}{10}) \times 15 = 30 + \frac{7 \times 15}{10} = 30 + 10.5 = 40.5$

Q 4 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

Numbers announced Number of times

0-15 8

15-30 9

30-45 10

45-60 12

60-75 9

Based on the above information, answer the following:

(iv) Find mode of the given data.

0%

(51)

Since the highest frequency is 12 which belongs to 45 – 60, therefore modal class is 45 – 60

Here, $l = 45, f_{0} = 10, f_{1} = 12, f_{2} = 9, h = 15$

$Mode = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h = 45 + \frac{12 - 10}{24 - 10 - 9} \times 15 = 45 + \frac{2}{5} \times 15 = 45 + 6 = 51$

Q 5 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said ‘BINGO’.

Numbers announced

Number of times

0 – 15

8

15 – 30

9

30 – 45

10

45 – 60

12

60 – 75

9

Based on the above information, answer the following questions:

(i) Write the median class.

Numbers announced	Number of times
0 – 15	8
15 – 30	9
30 – 45	10
45 – 60	12
60 – 75	9

30 – 45
15 – 30
45 – 60
60 – 75

1

2

3

4

(1)

We have,

Numbers announced	Number of times	Cumulative Frequency
0 – 15	8	8
15 – 30	9	17
30 – 45	10	27
45 – 60	12	39
60 – 75	9	48

$H e r e, n = 48 \Rightarrow n / 2 = 48 / 2 = 24 ∴ T h e m e d i a n c l a s s i s 30 - 45$

Q 6 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said ‘BINGO’.

Numbers announced

Number of times

0 – 15

8

15 – 30

9

30 – 45

10

45 – 60

12

60 – 75

9

Based on the above information, answer the following questions:

(ii) What is the modal class?

Numbers announced	Number of times
0 – 15	8
15 – 30	9
30 – 45	10
45 – 60	12
60 – 75	9

15 – 35
45 – 60
60 – 75
0 – 15

1

2

3

4

(2)

Since 12 is the maximum frequency, 45 – 60 is the modal class

Q 7 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said ‘BINGO’.

Numbers announced

Number of times

0 – 15

8

15 – 30

9

30 – 45

10

45 – 60

12

60 – 75

9

Based on the above information, answer the following questions:

(iii) (a) Find median of the given data.

Numbers announced	Number of times
0 – 15	8
15 – 30	9
30 – 45	10
45 – 60	12
60 – 75	9

40.5
35.5
36.5
39.5

1

2

3

4

(1)

The median class is 30 – 45.

$H e r e, n / 2 = 24, l = 30, c f = 17, f = 10, h = 15 ∴ M e d i a n = l + (\frac{\frac{n}{2} - c f}{f}) \times h = 30 + (\frac{24 - 17}{10}) \times 15 = 30 + \frac{105}{10} = 40.5 T h e m e d i a n o f t h e g i v e n d a t a i s 40.5 .$

Q 8 :

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

The table given below, shows the data of one such game where 48 balls were used before Tara said ‘BINGO’.

Numbers announced

Number of times

0 – 15

8

15 – 30

9

30 – 45

10

45 – 60

12

60 – 75

9

Based on the above information, answer the following questions:

(iii) (b) Find mode of the given data

Numbers announced	Number of times
0 – 15	8
15 – 30	9
30 – 45	10
45 – 60	12
60 – 75	9

50
45
46
51

1

2

3

4

(4)

Here, the maximum frequency is 12 and the class corresponding to this frequency is 45 – 60

$S o, l = 45, f_{1} = 12, f_{0} = 10, f_{2} = 9, h = 15 ∴ Mode = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h = 45 + (\frac{12 - 10}{2 \times 12 - 10 - 9}) \times 15 = 45 + \frac{30}{5} = 51 T h e m o d e o f t h e g i v e n d a t a i s 51 .$

Q 9 :

A stopwatch was used to time a 100-metre race run by a group of students. The sports teacher carefully recorded their times in seconds, which are presented in the table below.

Time (in seconds)

0 – 20

20 – 40

40 – 60

60 – 80

80 – 100

Number of students

8

10

13

6

3

Based on the above information, answer the following questions:

(i) Find the lower limit of the modal class.

Time (in seconds)	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Number of students	8	10	13	6	3

40
30
25
15

1

2

3

4

(1)

Highest frequency = 13
∴ Modal class = 40 – 60

So, lower limit of the modal class = 40

Q 10 :

A stopwatch was used to time a 100-metre race run by a group of students. The sports teacher carefully recorded their times in seconds, which are presented in the table below.

Time (in seconds)

0 – 20

20 – 40

40 – 60

60 – 80

80 – 100

Number of students

8

10

13

6

3

Based on the above information, answer the following questions:

(ii) How many students finished the race after 1 minute?

Time (in seconds)	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Number of students	8	10	13	6	3

8
9
7
5

1

2

3

4

(2)

Number of students who finished the race after 1 minute
= 6 + 3 = 9

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