# Important Questions for CBSE Class 10 Maths Chapter 14 - Statistics 2 Mark Question

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CBSE Class 10 Maths Chapter-14 Statistics Important Questions

## 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 Mo is given by
Mo =

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 M0 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 =