Account
It's free!

User


Login
Register


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

R.D. Sharma solutions 10 Mathematics chapter 7 Statistics

Chapters

R.D. Sharma 10 Mathematics

10 Mathematics

Chapter 7 - Statistics

Page 0

Calculate the mean for the following distribution:-

x 5 6 7 8 9
f 4 8 14 11 3

Calculate the mean for the following distribution:-

x 5 6 7 8 9
f 4 8 14 11 3

Find the mean of the following data:-

x 19 21 23 25 27 29 31
f 13 15 16 18 16 15 13

Find the mean of the following data:-

x 19 21 23 25 27 29 31
f 13 15 16 18 16 15 13

If the mean of the following data is 20.6. Find the value of p.

x 10 15 P 25 35
f 3 10 25 7 5

If the mean of the following data is 20.6. Find the value of p.

x 10 15 P 25 35
f 3 10 25 7 5

If the mean of the following data is 15, find p.

x 5 10 15 20 25
f 6 P 6 10 5

If the mean of the following data is 15, find p.

x 5 10 15 20 25
f 6 P 6 10 5

Find the value of p for the following distribution whose mean is 16.6

x 8 12 15 P 20 25 30
f 12 16 20 24 16 8 4

Find the value of p for the following distribution whose mean is 16.6

x 8 12 15 P 20 25 30
f 12 16 20 24 16 8 4

Find the missing value of p for the following distribution whose mean is 12.58

x 5 8 10 12 P 20 25
f 2 5 8 22 7 4 2

Find the missing value of p for the following distribution whose mean is 12.58

x 5 8 10 12 P 20 25
f 2 5 8 22 7 4 2

Find the missing frequency (p) for the following distribution whose mean is 7.68.

x 3 5 7 9 11 13
f 6 8 15 P 8 4

Find the missing frequency (p) for the following distribution whose mean is 7.68.

x 3 5 7 9 11 13
f 6 8 15 P 8 4

Find the value of p, if the mean of the following distribution is 20.

x 15 17 19 20+P 23
f 2 3 4 5P 6

Find the value of p, if the mean of the following distribution is 20.

x 15 17 19 20+P 23
f 2 3 4 5P 6

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students

Age (in years) 15 16 17 18 19 20
No. of students 3 8 10 10 5 4

The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students

Age (in years) 15 16 17 18 19 20
No. of students 3 8 10 10 5 4

Candidates of four schools appear in a mathematics test. The data were as follows:-

Schools No. of Candidates Average Score
I 60 75
II 48 80
III NA 55
IV 40 50

If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.

Candidates of four schools appear in a mathematics test. The data were as follows:-

Schools No. of Candidates Average Score
I 60 75
II 48 80
III NA 55
IV 40 50

If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss No. of tosses
0 38
1 144
2 342
3 287
4 164
5 25
Total 1000

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss No. of tosses
0 38
1 144
2 342
3 287
4 164
5 25
Total 1000

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x 10 30 50 70 90  
f 17 f1 32 f2 19 Total 120

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x 10 30 50 70 90  
f 17 f1 32 f2 19 Total 120

The arithmetic mean of the following data is 14. Find the value of k

x1 5 10 15 20 25
f1 7 k 8 4 5

The arithmetic mean of the following data is 14. Find the value of k

x1 5 10 15 20 25
f1 7 k 8 4 5

The arithmetic mean of the following data is 25, find the value of k.

x1 5 15 25 35 45
f1 3 k 3 6 2

The arithmetic mean of the following data is 25, find the value of k.

x1 5 15 25 35 45
f1 3 k 3 6 2

If the mean of the following data is 18.75. Find the value of p.

x 10 15 P 25 30
f 5 10 7 8 2

If the mean of the following data is 18.75. Find the value of p.

x 10 15 P 25 30
f 5 10 7 8 2

Page 0

The number of telephone calls received at an exchange per interval for 250 successive one minute
intervals are given in the following frequency table:

No. of calls(x) 0 1 2 3 4 5 6
No. of intervals (f) 15 24 29 46 54 43 39

Compute the mean number of calls per interval.

The number of telephone calls received at an exchange per interval for 250 successive one minute
intervals are given in the following frequency table:

No. of calls(x) 0 1 2 3 4 5 6
No. of intervals (f) 15 24 29 46 54 43 39

Compute the mean number of calls per interval.

The following table gives the number of branches and number of plants in the garden of a school.

No. of branches (x) 2 3 4 5 6
No. of plants (f) 49 43 57 38 13

Calculate the average number of branches per plant.

The following table gives the number of branches and number of plants in the garden of a school.

No. of branches (x) 2 3 4 5 6
No. of plants (f) 49 43 57 38 13

Calculate the average number of branches per plant.

The following table gives the number of children of 150 families in a village. Find the average number of children per family.

No. of children (x) 0 1 2 3 4 5
No. of families (f) 10 21 55 42 15 7

The following table gives the number of children of 150 families in a village. Find the average number of children per family.

No. of children (x) 0 1 2 3 4 5
No. of families (f) 10 21 55 42 15 7

The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Marks(x) 15 20 22 24 25 30 33 38 45
Frequency (f) 5 8 11 20 23 18 13 3 1

Find the average number of marks.

The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Marks(x) 15 20 22 24 25 30 33 38 45
Frequency (f) 5 8 11 20 23 18 13 3 1

Find the average number of marks.

The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:

No. of students absent (x) 0 1 2 3 4 5 6 7
No. of days (f) 1 4 10 50 34 15 4 2

Find the mean number of students absent per day.

The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:

No. of students absent (x) 0 1 2 3 4 5 6 7
No. of days (f) 1 4 10 50 34 15 4 2

Find the mean number of students absent per day.

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:

No. of misprints per page (x) 0 1 2 3 4 5
No. of pages (f) 154 95 36 9 5 1

Find the average number of misprints per page.

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:

No. of misprints per page (x) 0 1 2 3 4 5
No. of pages (f) 154 95 36 9 5 1

Find the average number of misprints per page.

The following distribution gives the number of accidents met by 160 workers in a factory during a month.

No. of accidents(x) 0 1 2 3 4
No. of workers (f) 70 52 34 3 1

Find the average number of accidents per worker.

The following distribution gives the number of accidents met by 160 workers in a factory during a month.

No. of accidents(x) 0 1 2 3 4
No. of workers (f) 70 52 34 3 1

Find the average number of accidents per worker.

Find the mean from the following frequency distribution of marks at a test in statistics:

Marks(x) 5 10 15 20 25 30 35 40 45 50
No. of students (f) 15 50 80 76 72 45 39 9 8 6

Find the mean from the following frequency distribution of marks at a test in statistics:

Marks(x) 5 10 15 20 25 30 35 40 45 50
No. of students (f) 15 50 80 76 72 45 39 9 8 6

Page 0

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city. Find the average expenditure (in rupees) per household.

Expenditure
(in rupees) (x1)
Frequency(f1)
100 - 150 24
150 - 200 40
200 - 250 33
250 - 300 28
300 - 350 30
350 - 400 22
400 - 450 16
450 - 500 7

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city. Find the average expenditure (in rupees) per household.

Expenditure
(in rupees) (x1)
Frequency(f1)
100 - 150 24
150 - 200 40
200 - 250 33
250 - 300 28
300 - 350 30
350 - 400 22
400 - 450 16
450 - 500 7

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?

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?

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.

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.

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

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

Find the mean of each of the following frequency distributions: (5 - 14)

Class interval 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30
Frequency 6 8 10 9 7

Find the mean of each of the following frequency distributions: (5 - 14)

Class interval 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30
Frequency 6 8 10 9 7

Find the mean of each of the following frequency distributions

Class interval 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 150 - 170
Frequency 18 12 13 27 8 22

Find the mean of each of the following frequency distributions

Class interval 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 150 - 170
Frequency 18 12 13 27 8 22

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 6 7 10 8 9

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 6 7 10 8 9

Find the mean of each of the following frequency distributions

Class interval 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30
Frequency 7 5 10 12 6

Find the mean of each of the following frequency distributions

Class interval 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30
Frequency 7 5 10 12 6

Find the mean of each of the following frequency distributions

Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 9 12 15 10 14

Find the mean of each of the following frequency distributions

Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 9 12 15 10 14

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 5 9 10 8 8

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 5 9 10 8 8

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 5 6 4 3 2

Find the mean of each of the following frequency distributions

Class interval 0 - 8 8 - 16 16 - 24 24 - 32 32 - 40
Frequency 5 6 4 3 2

Find the mean of each of the following frequency distributions

Class interval 10 - 30 30 - 50 50 - 70 70 - 90 90 - 110 110 - 130
Frequency 5 8 12 20 3 2

Find the mean of each of the following frequency distributions

Class interval 10 - 30 30 - 50 50 - 70 70 - 90 90 - 110 110 - 130
Frequency 5 8 12 20 3 2

Find the mean of each of the following frequency distributions

Class interval 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75
Frequency 6 10 8 12 4

Find the mean of each of the following frequency distributions

Class interval 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75
Frequency 6 10 8 12 4

Find the mean of each of the following frequency distributions

Classes 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59
Frequency 14 22 16 6 5 3 4

Find the mean of each of the following frequency distributions

Classes 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59
Frequency 14 22 16 6 5 3 4

For the following distribution, calculate mean using all suitable methods:

Size of item 1 - 4 4 - 9 9 - 16 16 - 27
Frequency 6 12 26 20

For the following distribution, calculate mean using all suitable methods:

Size of item 1 - 4 4 - 9 9 - 16 16 - 27
Frequency 6 12 26 20

The weekly observations on cost of living index in a certain city for the year 2004 - 2005 are given below. Compute the weekly cost of living index.

Cost of living Index Number of Students
1400 - 1500 5
1500 - 1600 10
1600 - 1700 20
1700 - 1800 9
1800 - 1900 6
1900 - 2000 2

The weekly observations on cost of living index in a certain city for the year 2004 - 2005 are given below. Compute the weekly cost of living index.

Cost of living Index Number of Students
1400 - 1500 5
1500 - 1600 10
1600 - 1700 20
1700 - 1800 9
1800 - 1900 6
1900 - 2000 2

The following table shows the marks scored by 140 students in an examination of a certain paper:

Marks: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Number of students: 20 24 40 36 20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

The following table shows the marks scored by 140 students in an examination of a certain paper:

Marks: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Number of students: 20 24 40 36 20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2.

Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120
Frequency 5 f1 10 f2 7 8

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2.

Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120
Frequency 5 f1 10 f2 7 8

The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.

Class interval 11 - 13 13 - 15 15 - 17 17 - 19 19 - 21 21 - 23 23 - 25
Frequency 7 6 9 13 - 5 4

The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.

Class interval 11 - 13 13 - 15 15 - 17 17 - 19 19 - 21 21 - 23 23 - 25
Frequency 7 6 9 13 - 5 4

If the mean of the following distribution is 27, find the value of p.

Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 8 p 12 13 10

If the mean of the following distribution is 27, find the value of p.

Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 8 p 12 13 10

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?

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?

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.

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.

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.

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.

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

 

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

 

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

 

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

 

Page 0

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:

715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.

Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:

715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.

The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): 160 - 162 163 - 165 166 - 168 169 - 171 172 - 174
No. of students: 15 118 142 127 18

Find the median height.

The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): 160 - 162 163 - 165 166 - 168 169 - 171 172 - 174
No. of students: 15 118 142 127 18

Find the median height.

Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.: 55 - 64 65 - 74 75 - 84 85 - 94 95 - 104 105 - 114 115 - 124 125 - 134 135 - 144
No of Students: 1 2 9 22 33 22 8 2 1

Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.: 55 - 64 65 - 74 75 - 84 85 - 94 95 - 104 105 - 114 115 - 124 125 - 134 135 - 144
No of Students: 1 2 9 22 33 22 8 2 1

Calculate the median from the following data:

Rent (in Rs.): 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95
No. of Houses: 8 10 15 25 40 20 15 7

Calculate the median from the following data:

Rent (in Rs.): 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95
No. of Houses: 8 10 15 25 40 20 15 7

Calculate the median from the following data:

Marks below: 10 20 30 40 50 60 70 80
No. of students: 15 35 60 84 96 127 198 250

Calculate the median from the following data:

Marks below: 10 20 30 40 50 60 70 80
No. of students: 15 35 60 84 96 127 198 250

An incomplete distribution is given as follows:

Variable: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15

You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

An incomplete distribution is given as follows:

Variable: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15

You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
No. of persons 5 25 ? 18 7

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
No. of persons 5 25 ? 18 7

Find the missing frequencies and the median for the following distribution if the mean is 1.46.

No. of accidents: 0 1 2 3 4 5 Total
Frequency (No. of days): 46 ? ? 25 10 5 200

Find the missing frequencies and the median for the following distribution if the mean is 1.46.

No. of accidents: 0 1 2 3 4 5 Total
Frequency (No. of days): 46 ? ? 25 10 5 200

An incomplete distribution is given below:

Variable: 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency: 12 30 - 65 - 25 18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

An incomplete distribution is given below:

Variable: 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency: 12 30 - 65 - 25 18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

The following table gives the frequency distribution of married women by age at marriage:

Age (in years) Frequency
15-19 53
20-24 140
25-29 98
30-34 32
35-39 12
40-44 9
45-49 5
50-54 3
55-59 3
60 and above 2

Calculate the median and interpret the results.

The following table gives the frequency distribution of married women by age at marriage:

Age (in years) Frequency
15-19 53
20-24 140
25-29 98
30-34 32
35-39 12
40-44 9
45-49 5
50-54 3
55-59 3
60 and above 2

Calculate the median and interpret the results.

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

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

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:

Class interval Frequency
0 - 100 2
100 - 200 5
200 - 300 f1
300 - 400 12
400 - 500 17
500 - 600 20
600 - 700 f2
700 - 800 9
800 - 900 7
900 - 1000 4

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:

Class interval Frequency
0 - 100 2
100 - 200 5
200 - 300 f1
300 - 400 12
400 - 500 17
500 - 600 20
600 - 700 f2
700 - 800 9
800 - 900 7
900 - 1000 4

If the median of the following data is 32.5, find the missing frequencies.

Class interval: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Total
Frequency: f1 5 9 12 f2 3 2 40

If the median of the following data is 32.5, find the missing frequencies.

Class interval: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Total
Frequency: f1 5 9 12 f2 3 2 40

Compute the median for the following data:

Marks No. of students
Less than 10 0
Less than 30 10
Less than 50 25
Less than 70 43
Less than 90 65
Less than 110 87
Less than 130 96
Less than 150 100

Compute the median for the following data:

Marks No. of students
Less than 10 0
Less than 30 10
Less than 50 25
Less than 70 43
Less than 90 65
Less than 110 87
Less than 130 96
Less than 150 100

Compute the median for the following data:

Marks No. of students
More than 150 0
More than 140 12
More than 130 27
More than 120 60
More than 110 105
More than 100 124
More than 90 141
More than 80 150

Compute the median for the following data:

Marks No. of students
More than 150 0
More than 140 12
More than 130 27
More than 120 60
More than 110 105
More than 100 124
More than 90 141
More than 80 150

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm Number of Girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Less than 165 51

Find the median height.

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm Number of Girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Less than 165 51

Find the median height.

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

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm)

Number or leaves fi

118 − 126

3

127 − 135

5

136 − 144

9

145 − 153

12

154 − 162

5

163 − 171

4

172 − 180

2

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm)

Number or leaves fi

118 − 126

3

127 − 135

5

136 − 144

9

145 − 153

12

154 − 162

5

163 − 171

4

172 − 180

2

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)

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.

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.

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

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

Page 0

Find the mode of the following data:

3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4

Find the mode of the following data:

3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4

Find the mode of the following data:

15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15

The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:

Shirt size: 37 38 39 40 41 42 43 44
Number of persons: 15 25 39 41 36 17 15 12

Find the model shirt size worn by the group.

Find the mode of the following distribution.

Class-interval: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
Frequency: 5 8 7 12 28 20 10 10

 

Find the mode of the following distribution.

Class-interval: 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40
Frequency: 30 45 75 35 25 15

 

Find the mode of the following distribution.

Class-interval: 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 50 - 55
Frequency: 25 34 50 42 38 14

 

Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years): 16-18 18-20 20-22 22-24 24-26
Group A: 50 78 46 28 23
Group B: 54 89 40 25 17

The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.

Marks: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
Frequency: 3 5 16 12 13 20 5 4 1 1

 

The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): 160 - 162 163 - 165 166 - 168 169 - 171 172 - 174
No. of students: 15 118 142 127 18

Find the average height of maximum number of students.

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.

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.

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

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

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.

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

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

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.

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.

Find the mean, median and mode of the following data:

Classes: 0-20 20-40 40-60 40-60 80-100 100-120 120-140
Frequency: 6 8 10 12 6 5 3

 

Find the mean, median and mode of the following data:

Classes: 0 - 50 50 - 100 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350
Frequency: 2 3 5 6 5 3 1

 

The following table 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

Find the mean, mode and median of the above data.

Page 0

Draw an ogive by less than method for the following data:

No. of rooms: 1 2 3 4 5 6 7 8 9 10
No. of houses: 4 9 22 28 24 12 8 6 5 2

 

Draw an ogive by less than method for the following data:

No. of rooms: 1 2 3 4 5 6 7 8 9 10
No. of houses: 4 9 22 28 24 12 8 6 5 2

 

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks No. of students
600 - 640 16
640 - 680 45
680 - 720 156
720 - 760 284
760 - 800 172
800 - 840 59
840 - 880 18

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks No. of students
600 - 640 16
640 - 680 45
680 - 720 156
720 - 760 284
760 - 800 172
800 - 840 59
840 - 880 18

Draw an ogive to represent the following frequency distribution:

Class-interval: 0 - 4 5 - 9 10 - 14 15 - 19 20 - 24
Frequency: 2 6 10 5 3

Draw an ogive to represent the following frequency distribution:

Class-interval: 0 - 4 5 - 9 10 - 14 15 - 19 20 - 24
Frequency: 2 6 10 5 3

The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop: 0 - 50 50 - 100 100 - 150 150 - 200 200 - 250 250 - 300
No. of shops: 12 18 27 20 17 6

Draw the frequency polygon for it.

The following table gives the height of trees:
 

Height No. of trees
Less than 7
Less than 14
Less than 21
Less than 28
Less than 35
Less than 42
Less than 49
Less than 56
26
57
92
134
216
287
341
360


Draw 'less than' ogive and 'more than' ogive.

 

The following table gives the height of trees:
 

Height No. of trees
Less than 7
Less than 14
Less than 21
Less than 28
Less than 35
Less than 42
Less than 49
Less than 56
26
57
92
134
216
287
341
360


Draw 'less than' ogive and 'more than' ogive.

 

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:
 

Profit (in lakhs in Rs) Number of shops (frequency)
More than or equal to 5
More than or equal to 10
More than or equal to 15
More than or equal to 20
More than or equal to 25
More than or equal to 30
More than or equal to 35
30
28
16
14
10
7
3


Draw both ogives for the above data and hence obtain the median.

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:
 

Profit (in lakhs in Rs) Number of shops (frequency)
More than or equal to 5
More than or equal to 10
More than or equal to 15
More than or equal to 20
More than or equal to 25
More than or equal to 30
More than or equal to 35
30
28
16
14
10
7
3


Draw both ogives for the above data and hence obtain the median.

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.

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

Production yield in kg per hectare: 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80
Number of farms: 2 8 12 24 38 16

Draw ‘less than’ ogive and ‘more than’ ogive.

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

Production yield in kg per hectare: 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80
Number of farms: 2 8 12 24 38 16

Draw ‘less than’ ogive and ‘more than’ ogive.

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.

R.D. Sharma 10 Mathematics

10 Mathematics

R.D. Sharma solutions for Class 10


S