## CBSE Class 10 Maths Chapter-14 Statistics – Free PDF Download

Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 14 – Statistics prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination.

CBSE Class 10 Maths Chapter-14 Statistics Important Questions

**CBSE Class 10 Maths Important Questions Chapter 14 – Statistics**

**2 Mark Questions**

**1. The following data gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of students:**

Age (in years) | 15 | 16 | 17 | 18 | 19 | 20 |

No. of student | 3 | 8 | 10 | 10 | 5 | 4 |

**Ans.** We have

Age (in years) (x) | No. of students (f) | fx |

15 | 3 | 45 |

16 | 8 | 128 |

17 | 10 | 170 |

18 | 10 | 180 |

19 | 5 | 95 |

20 | 4 | 80 |

Mean years

**2. For the following grouped frequency distribution, find the mode.**

Class | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21 | 21-24 |

Frequency | 2 | 5 | 10 | 23 | 21 | 12 | 3 |

**Ans.** Since the maximum frequency = 23 and it corresponds to the class 12-15

Modal class = 12-15

**3. Construct the cumulative frequency distribution of the following distribution:**

Class | 12.5-17.5 | 17.5-22.5 | 22.5-27.5 | 27.5-32.5 | 32.5-37.5 |

Frequency | 2 | 22 | 19 | 14 | 13 |

**Ans. **The required cumulative frequency distribution of the given distribution is given below:

Class | Frequency | Cumulative frequency |

12.5-17.5 | 2 | 2 |

17.5-22.5 | 22 | 24 |

22.5-27.5 | 19 | 43 |

27.5-32.5 | 14 | 57 |

32.5-37.5 | 13 | 70 |

**4. The median and mode of a distribution are 21.2 and 21.4 respectively, find its mean.**

**Ans.** We know that Mean = Mode + (Median – Mode)

**5. The marks distribution of 30 students in a mathematics examination are given below**

Class Interval | 10-25 | 25-40 | 40-55 | 55-70 | 70-85 | 85-100 |

No. of students | 2 | 3 | 7 | 6 | 0 | 6 |

**Ans.** Since the maximum frequency = 7 and it corresponds to the class 40-55.

The modal class= 40-55

Here,

We know that mode M_{o} is given by

M_{o} =

Thus, Mode marks = 52

**6. Find the mode of this data.**

**Construct the cumulative frequency distribution of following distribution:**

Marks | 39.5-49.5 | 49.5-59.5 | 59.5-69.5 | 69.5-79.5 | 79.5-89.5 | 89.5-99.5 |

Students | 5 | 10 | 20 | 30 | 20 | 15 |

**Ans.** The required cumulative frequency distribution of the given distribution is given below.

Marks | No. of Students | Cumulative Frequency |

39.5-49.5 | 5 | 5 |

49.5-59.5 | 10 | 15 |

59.5-69.5 | 20 | 35 |

69.5-79.5 | 30 | 65 |

79.5-89.5 | 20 | 85 |

89.5-99.5 | 15 | 100 |

**7. If the values of mean and mode are respectively 30 and 15, then median =**

**(a) 22.5**

**(b) 24.5**

**(c) 25**

**(d) 26 Ans. **Median = Mode(Mean – Mode)

**8. If the mean of the following data is 18.75. find the value of P.**

10 | 15 | P | 25 | 30 | |

5 | 10 | 7 | 8 | 2 |

**Ans.** We have

10 | 5 | 50 |

15 | 10 | 150 |

P | 7 | 7P |

25 | 8 | 200 |

30 | 2 | 60 |

Now mean = 18.75

**9. Find the mean of the following data.**

Classes | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Frequency | 5 | 8 | 13 | 15 | 9 |

**Ans.** We have

Classes | Mid-value | Frequency | |

10-20 | 15 | 5 | 75 |

20-30 | 25 | 8 | 200 |

30-40 | 35 | 13 | 455 |

40-50 | 45 | 15 | 675 |

50-60 | 55 | 9 | 495 |

Now mean

Hence, mean

**10. The following data gives the information observed life times (in hours) of 225 electrical components. Determine the modal life times of the components.**

Life time (in hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-200 |

Frequency | 10 | 35 | 52 | 61 | 38 | 29 |

**Ans.** Since the maximum frequency = 61 and it corresponds to the class 60-80

Modal class = 60-80

Here,

We know that mode Mo is given by

Thus, modal life times = 65.625 hours

**11. Construct the cumulative frequency distribution of the following distribution:**

Class Interval | 6.5-7.5 | 7.5-8.5 | 8.5-9.5 | 9.5-10.5 | 10.5-11.5 | 11.5-12.5 | 12.5-13.5 |

Frequency | 5 | 12 | 25 | 48 | 32 | 6 | 1 |

**Ans.** The required cumulative frequency distribution of the given distribution is given below:

Class Interval | Frequency | Cumulative Frequency |

6.5-7.5 | 5 | 5 |

7.5-8.5 | 12 | 17 |

8.5-9.5 | 25 | 42 |

9.5-10.5 | 48 | 90 |

10.5-11.5 | 32 | 122 |

11.5-12.5 | 6 | 128 |

12.5-13.5 | 1 | 129 |

**12. Calculate the median from the following data:**

Marks | 0-10 | 10-30 | 30-60 | 60-80 | 80-100 |

No. of students | 5 | 15 | 30 | 8 | 2 |

**Ans.** We have

Marks | No. of students (f) | C.F |

0-10 | 5 | 5 |

10-30 | 15 | 20 |

30-60 | 30 | 50 |

60-80 | 8 | 58 |

80-100 | 2 | 60 |

Since which his in the class 30-60

Median class is 30-60

We know that median Me is given by

Here,

= 30 +10= 40

Hence, median = 40

**13. Find the mean of the following data:**

Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency | 3 | 5 | 9 | 5 | 3 |

**Ans. **We have

Classes | Mid-value | Frequency | |

0-10 | 5 | 3 | 15 |

10-20 | 15 | 5 | 75 |

20-30 | 25 | 9 | 225 |

30-40 | 35 | 5 | 175 |

40-50 | 45 | 3 | 135 |

Now Mean

**14. A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. Find the mode.**

Family size | 1-3 | 3-5 | 5-7 | 7-9 | 9-11 |

No. of families | 7 | 8 | 2 | 4 | 1 |

**Ans.** Since the maximum frequency = 8 and it corresponds to the class 3-5

Modal class = 3-5

Here,

We know that mode Mo is given by

**15. Construct the cumulative frequency distribution of the following distribution:**

Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Frequency | 5 | 3 | 10 | 6 | 4 | 2 |

**Ans.** The required cumulative frequency distribution of the given distribution is given below:

Class Interval | Frequency (f) | Cumulative frequency |

0-10 | 5 | 5 |

10-20 | 3 | 8 |

20-30 | 10 | 18 |

30-40 | 6 | 24 |

40-50 | 4 | 28 |

50-60 | 2 | 30 |

Total | N= 30 |

**16. If the values of mean and median are 26.4 and 27.2, what will be the value of mode?**

**Ans.** We know that

Mode = 3 median -2 mean

= 3(27.2) – 2(26.4)

= 81.6 – 52.8 = 28.8

Mode = 28.8

**17. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students.**

Marks obtained | 10 | 20 | 36 | 40 | 50 | 56 | 60 | 70 | 72 | 80 | 88 | 92 | 98 |

students | 1 | 1 | 3 | 4 | 3 | 2 | 4 | 4 | 1 | 1 | 2 | 3 | 1 |

**Ans.**

Marks obtained | No. of students | |

10 | 1 | 10 |

20 | 1 | 20 |

36 | 3 | 108 |

40 | 4 | 160 |

50 | 3 | 150 |

56 | 2 | 112 |

60 | 4 | 240 |

70 | 4 | 280 |

72 | 1 | 72 |

80 | 1 | 80 |

88 | 2 | 176 |

92 | 3 | 276 |

95 | 1 | 95 |

Mean =

Thus, mean = 59.3

**18. A student noted the numbers of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized in the table given below. Find the mode of the data.**

No. of cars | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |

**Ans. **Since the maximum frequency = 20

And it corresponds to the class 40-50

Modal class = 40-50

Here,

We know that mode M_{0} is given by

**19. Construct the cumulative frequency distribution of the following distribution:**

consumption (units) | 65-85 | 85-105 | 105-125 | 125-145 | 145-165 | 165-185 |

Consumers | 4 | 5 | 12 | 20 | 14 | 8 |

**Ans. **The required accumulative frequency distribution of the given distribution is given below.

Monthly consumption (in units) | No. of consumes | Cumulative frequency |

65-85 | 4 | 4 |

85-105 | 5 | 9 |

105-125 | 13 | 22 |

125-145 | 20 | 42 |

145-165 | 14 | 56 |

165-185 | 8 | 64 |

N = 64 |

**20. If the values of mean and median are 53.6 and 55.81, what will be the value of mode?**

**Ans.** We know that

Mode = 3 Median – 2 mean

Mean =