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NCERT solutions Mathematics Class 10 chapter 14 Statistics

Chapters

NCERT Mathematics Class 10

Mathematics Textbook for Class 10

Chapter 14 - Statistics

Pages 270 - 272

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14
Number of houses 1 2 1 5 6 2 3

Which method did you use for finding the mean, and why?

Q 1 | Page 270

Consider the following distribution of daily wages of 50 worker of a factory.

Daily wages (in Rs)

100­ − 120

120­ − 140

140 −1 60

160 − 180

180 − 200

Number of workers

12

14

8

6

10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Q 2 | Page 270

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

Daily pocket allowance (in Rs 11­ − 13 13­ − 15 15 −17 17 − 19 19 − 21 21 − 23 23 − 25
Number of workers 7 6 9 13 f 5 4
Q 3 | Page 270

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Fine the mean heart beats per minute for these women, choosing a suitable method.

 

Number of heart beats per minute 65 − 68 68­ − 71 71 −74 74 − 77 77 − 80 80 − 83 83 − 86
Number of women 2 4 3 8 7 4 2
Q 4 | Page 271

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoe 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64
Number of boxes 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Q 5 | Page 271

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure (in Rs) 100 − 150 150 − 200 200 − 250 250 − 300 300 − 350
Number of households 4 5 12 2 2

Find the mean daily expenditure on food by a suitable method.

Q 6 | Page 271

To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

concentration of SO2 (in ppm) Frequency
0.00 − 0.04 4
0.04 − 0.08 9
0.08 − 0.12 9
0.12 − 0.16 2
0.16 − 0.20 4
0.20 − 0.24 2

Find the mean concentration of SO2 in the air.

Q 7 | Page 271

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days 0 − 6 6 − 10 10 − 14 14 − 20 20 − 28 28 − 38 38 − 40
Number of students 11 10 7 4 4 3 1

 

Q 8 | Page 272

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate

Literacy rate (in %) 45 − 55 55 − 65 65 − 75 75 − 85 85 − 95
Number of cities 3 10 11 8 3

 

Q 9 | Page 272

Pages 275 - 276

The following table shows the ages of the patients admitted in a hospital during a year:

age (in years)

5 − 15

15 − 25

25 − 35

35 − 45

45 − 55

55 − 65

Number of patients

6

11

21

23

14

5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Q 1 | Page 275

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours) 0 − 20 20 − 40 40 − 60 60 − 80 80 − 100 100 − 120
Frequency 10 35 52 61 38 29

Determine the modal lifetimes of the components.

Q 2 | Page 275

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs) Number of families
1000 − 1500 24
1500 − 2000 40
2000 − 2500 33
2500 − 3000 28
3000 − 3500 30
3500 − 4000 22
4000 − 4500 16
4500 − 5000 7
Q 3 | Page 275

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher Number of states/U.T
15 − 20 3
20 − 25 8
25 − 30 9
30 − 35 10
35 − 40 3
40 − 45 0
45 − 50 0
50 − 55 2
Q 4 | Page 276

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches

Runs scored Number of batsmen
3000 − 4000 4
4000 − 5000 18
5000 − 6000 9
6000 − 7000 7
7000 − 8000 6
8000 − 9000 3
9000 − 10000 1
10000 − 11000 1

Find the mode of the data.

Q 5 | Page 276

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

Number 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
Q 6 | Page 276

Pages 287 - 289

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption (in units) Number of consumers
65 - 85 4
85 - 105 5
105 - 125 13
125 - 145 20
145 - 165 14
165 - 185 8
185 - 205 4
Q 1 | Page 287

If the median of the distribution is given below is 28.5, find the values of x and y

Class interval Frequency
0 - 10 5
10 - 20 x
20 - 30 20
30 - 40 15
40 - 50 y
50 - 60 5
Total 60
Q 2 | Page 287

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.

Age (in years) Number of policy holders
Below 20 2
Below 25 6
Below 30 24
Below 35 45
Below 40 78
Below 45 89
Below 50 92
Below 55 98
Below 60 100
Q 3 | Page 287

Find the following table gives the distribution of the life time of 400 neon lamps

Life time (in hours) Number of lamps
1500 − 2000 14
2000 − 2500 56
2500 − 3000 60
3000 − 3500 86
3500 − 4000 74
4000 − 4500 62
4500 − 5000 48

Find the median life time of a lamp.

Q 5 | Page 289

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

 

Number of letters Number of surnames
1 - 4 6
4 − 7 30
7 - 10 40
10 - 13 6
13 - 16 4
16 − 19 4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Q 6 | Page 289

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg) 40 − 45 45 − 50 50 − 55 55 − 60 60 − 65 65 − 70 70 − 75
Number of students 2 3 8 6 6 3 2
Q 7 | Page 289

Page 293

The following distribution gives the daily income of 50 workers of a factory.

Daily income (in Rs 100 − 120 120 − 140 140 − 160 160 − 180 180 − 200
Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Q 1 | Page 293

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Weight (in kg Number of students
Less than 38 0
Less than 40 3
Less than 42 5
Less than 44 9
Less than 46 14
Less than 48 28
Less than 50 32
Less than 52 35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

Q 2 | Page 293

The following table gives production yield per hectare of wheat of 100 farms of a village.

Production yield (in kg/ha) 50 − 55 55 − 60 60 − 65 65 − 70 70 − 75 75 − 80
Number of farms 2 8 12 24 38 16

Change the distribution to a more than type distribution and draw ogive.

Q 3 | Page 293

NCERT Mathematics Class 10

Mathematics Textbook for Class 10
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