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# RD Sharma solutions for Class 10th Board Exam Mathematics chapter 7 - Statistics

## Chapter 7 : Statistics

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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

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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

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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

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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

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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.

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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 7Less than 14Less than 21Less than 28Less than 35Less than 42Less than 49Less than 56 265792134216287341360

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

The following table gives the height of trees:

 Height No. of trees Less than 7Less than 14Less than 21Less than 28Less than 35Less than 42Less than 49Less than 56 265792134216287341360

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 5More than or equal to 10More than or equal to 15More than or equal to 20More than or equal to 25More than or equal to 30More than or equal to 35 302816141073

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 5More than or equal to 10More than or equal to 15More than or equal to 20More than or equal to 25More than or equal to 30More than or equal to 35 302816141073

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.

## RD Sharma solutions for Class 10th Board Exam Mathematics chapter 7 - Statistics

RD Sharma solutions for Class 10th Board Exam Maths chapter 7 (Statistics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10th Board Exam Mathematics chapter 7 Statistics are Reading of Pie Diagram, Frequency Polygon, Tabulation of Data, Inclusive and Exclusive Type of Tables, Median of Grouped Data, Mean of Grouped Data, Histograms, Pie Diagram, Ogives (Cumulative Frequency Graphs), Applications of Ogives in Determination of Median, Relation Between Measures of Central Tendency, Introduction to Normal Distribution, Properties of Normal Distribution, Graphical Representation of Histograms, Graphical Representation of Cumulative Frequency Distribution, Mode of Grouped Data, Ogives (Cumulative Frequency Graphs), Mean of Grouped Data, Median of Grouped Data, Introduction of Statistics, Statistics Examples and Solutions.

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