# RS Aggarwal solutions for Secondary School Class 10 Maths chapter 9 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Latest edition]

#### Chapters ## Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 1

If the mean of 5 observation x, x + 2, x + 4, x + 6and x + 8 , find the value of x.

Q 2

If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean?

Q 3

Compute the mean for following data:

 Class 1-3 3-5 5-7 7-9 Frequency 12 22 27 19
Q 4

Find the mean using direct method:

 Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 7 5 6 12 8 2
Q 5

Find the mean of the following data, using direct method:

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

Find the mean of the following data, using direct method:

 Class 0-100 100-200 200-300 300-400 400-500 Frequency 6 9 15 12 8
Q 7

Using an appropriate method, find the mean of the following frequency distribution:

 Class 84-90 90-96 96-102 102-108 108-114 114-120 Frequency 8 10 16 23 12 11

Which method did you use, and why?

Q 8

If the mean of the following frequency distribution is 24, find the value of p.

 Class 0-10 10-20 20-30 30-40 40-50 Frequency 3 4 p 3 2
Q 9

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is ₹ 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 children 7 6 9 13 f 5 4
Q 10

The mean of following frequency distribution is 54. Find the value of p.

 Class 0-20 20-40 40-60 60-80 80-100 Frequency 7 p 10 9 13

Q 11

The mean of the following frequency data is 42, Find the missing frequencies x and y if the sum of frequencies is 100

 Class  interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 7 10 x 13 y 10 14 9

Find x and y.

Q 12

The daily expenditure of 100 families are given below. Calculate f_1 and f_2 if the mean daily expenditure is ₹ 188.

 Expenditure (in Rs) 140-160 160-180 180-200 200-220 220-240 Number of families 5 25 f_1 f_2 5
Q 13

Find the mean of the following frequency distribution is 57.6 and the total number of observation is 50.

 Class 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 7 f_1 12 f_2 8 5
Q 14

During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarized as follows:

 Number ofheartbeatsper minute 65 – 68 68 – 71 71 – 74 74 – 77 77 – 80 80 – 83 83 - 86 Number ofpatients 2 4 3 8 7 4 2

Find the mean heartbeats per minute for these patients, choosing a suitable method.

Q 15

Find the mean marks per student, using assumed-mean method:

 Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Number ofStudents 12 18 27 20 17 6
Q 16

Find the mean of the following frequency distribution, using the assumed-mean method:

 Class 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200 Frequency 10 20 30 15 5
Q 17

Find the mean of the following data, using assumed-mean method:

 Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 - 120 Frequency 20 35 52 44 38 31
Q 18

The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method .

 Literacyrate(%) 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95 Number ofcities 4 11 12 9 4
Q 19

Find the mean of the following frequency distribution using step-deviation method

 Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequency 7 10 15 8 10
Q 20

Find the mean of the following data, using step-deviation method:

 Class 5 – 15 15-20 20-35 35-45 45-55 55-65 65-75 Frequency 6 10 16 15 24 8 7
Q 21

The weights of tea in 70 packets are shown in the following table:

 Weight 200 –201 201 –202 202 –203 203 –204 204 –205 205 –206 Number of packets 13 27 18 10 1 1

Find the mean weight of packets using step deviation method.

Q 22

Find the mean of the following frequency distribution table using a suitable method:

 Class 20 – 30 30 – 40 40 – 50 50 – 60 60 - 70 Frequency 25 40 42 33 10
Q 23

In an annual examination, marks (out of 90) obtained by students of Class X in mathematics are given below:

 MarksObtained 0 – 15 15 – 30 30 – 45 45 – 60 60 – 75 75 – 90 Number ofstudents 2 4 5 20 9 10

Find the mean marks.

Q 24

Find the arithmetic mean of the following frequency distribution using step-deviation method:

 Age (in years) 18 – 24 24 – 30 30 – 36 36 – 42 42 – 48 48 – 54 Number of workers 6 8 12 8 4 2
Q 25

Find the mean of the following data using step-deviation method:

 Class 500 – 520 520 – 540 540 – 560 560 – 580 580 – 600 600 – 620 Frequency 14 9 5 4 3 5

Q 26

Find the mean age from the following frequency distribution:

 Age (in years) 25 – 29 30 – 34 35 – 39 40 – 44 45 – 49 50 – 54 55 – 59 Number of persons 4 14 22 16 6 5 3

Q 27

The following table shows the age distribution of patients of malaria in a village during a  particular month:

 Age (in years) 5 – 14 15 – 24 25 – 34 35 – 44 45 – 54 55 - 64 No. of cases 6 11 21 23 14 5

Find the average age of the patients.

Q 28

Weight of 60 eggs were recorded as given below:

 Weight (in grams) 75 – 79 80 – 84 85 – 89 90 – 94 95 – 99 100 - 104 105 - 109 No. of eggs 4 9 13 17 12 3 2

Calculate their mean weight to the nearest gram.

Q 29

The following table shows the marks scored by 80 students in an examination:

 Marks 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 No. ofstudents 3 10 25 49 65 73 78 80
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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 1

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.

 Age(in years) 0 – 15 15 – 30 30 – 45 45 – 60 60 - 75 No. of patients 5 20 40 50 25
Q 2

Compute mean from the following data:

 Marks 0 – 7 7 – 14 14 – 21 21 – 28 28 – 35 35 – 42 42 – 49 Number of Students 3 4 7 11 0 16 9
Q 3

The following table shows the daily wages of workers in a factory:

 Daily wages in (Rs) 0 – 100 100 – 200 200 – 300 300 – 400 400 – 500 Number of workers 40 32 48 22 8

Find the median daily wage income of the workers.

Q 4

Calculate the median from the following frequency distribution table:

 Class 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 Frequency 5 6 15 10 5 4 2 2

Q 5

Given below is the number of units of electricity consumed in a week in a certain locality:

 Class 65 – 85 85 – 105 105 – 125 125 – 145 145 – 165 165 – 185 185 – 200 Frequency 4 5 13 20 14 7 4

Calculate the median.

Q 6

Calculate the median from the following data:

 Height(in cm) 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 160 - 165 165 - 170 170 - 175 Frequency 6 10 18 22 20 15 6 3

Q 7

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

 Class 0 – 10 10 – 20 20 – 30 30 – 40 40 - 50 Frequency 5 25 ? 18 7

Q 8

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.

 Class 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 Frequency 12 a 12 15 b 6 6 4
Q 9

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y

 Runs scored 2500 – 3500 3500 – 4500 4500 – 5500 5500 – 6500 6500 – 7500 7500 - 8500 Number of batsman 5 x y 12 6 2

Q 10

If the median of the following frequency distribution is 32.5, find the values of f_1 and f_2.

 Class 0 – 10 10 – 20 20 – 30 30 -40 40 – 50 50 – 60 60 – 70 Total Frequency f_1 5 9 12 f_2 3 2 40

Q 11

Calculate the median for the following data:

 Class 19 – 25 26 – 32 33 – 39 40 – 46 47 – 53 54 - 60 Frequency 35 96 68 102 35 4

Q 12

Find the median wages for the following frequency distribution:

 Wages per day (in Rs) 61 – 70 71 – 80 81 – 90 91 – 100 101 – 110 111 – 120 No. of women workers 5 15 20 30 20 8

Q 13

Find the median from the following data:

 Class 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 35 – 40 40 – 45 Frequency 7 10 16 32 24 16 11 5 2

Q 14

Find the median from the following data:

 Marks No of students Below 10 12 Below 20 32 Below 30 57 Below 40 80 Below 50 92 Below 60 116 Below 70 164 Below 80 200
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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 1

Find the mode of the following distribution:

 Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 12 35 45 25 13
Q 2

Compute the mode of the following data:

 Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Frequency 25 16 28 20 5

Q 3

Heights of students of class X are givee in the flowing frequency distribution

 Height (in cm) 150 – 155 155 – 160 160 – 165 165 – 170 170 - 175 Number of students 15 8 20 12 5

Find the modal height.
Also, find the mean height. Compared and interpret the two measures of central tendency.

Q 4

Find the mode of the following distribution:

 Classinterval 10 – 14 14 – 18 18 – 22 22 – 26 26 – 30 30 – 34 34 – 38 38 – 42 Frequency 8 6 11 20 25 22 10 4

Q 5

Given below is the distribution of total household expenditure of 200 manual workers in a city:

 Expenditure (in Rs) 1000 – 1500 1500 – 2000 2000 – 2500 2500 – 3000 3000 – 3500 3500 – 4000 4000 – 4500 4500 – 5000 Number of manualworkers 24 40 31 28 32 23 17 5

Find the average expenditure done by maximum number of manual workers.

Q 6

Calculate the mode from the following data:

 Monthly salary (in Rs) No of employees 0 – 5000 90 5000 – 10000 150 10000 – 15000 100 15000 – 20000 80 20000 – 25000 70 25000 – 30000 10

Q 7

Compute the mode from the following data:

 Age (in years) 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 - 35 No of patients 6 11 18 24 17 13 5
Q 8

Compute the mode from the following series:

 Size 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95 95 – 105 105 - 115 Frequency 7 12 17 30 32 6 10

Q 9

Compute the mode from the following data:

 Class interval 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 41 – 45 46 – 50 Frequency 3 8 13 18 28 20 13 8 6 4
Q 10

The agewise participation of students in the annual function of a school is shown in the following distribution.

 Age (in years) 5 - 7 7 - 9 9 - 11 11 – 13 13 – 15 15 – 17 17 – 19 Number of students x 15 18 30 50 48 x

Find the missing frequencies when the sum of frequencies is 181. Also find the mode of the data.

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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 1

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

 Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 4 4 7 10 12 8 5
Q 2

Find the mean, median and mode of the following data

 Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 120 – 140 Frequency 6 8 10 12 6 5 3
Q 3

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

 Class 0 – 50 50 – 100 100 – 150 150 – 200 200 – 250 250 – 300 300 - 350 Frequency 2 3 5 6 5 3 1

Q 4

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

 Marks obtained 25 - 35 35 – 45 45 – 55 55 – 65 65 – 75 75 - 85 No. of students 7 31 33 17 11 1

Q 5

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:

 Height incm 120 – 130 130 – 140 140 – 150 150 – 160 160 – 170 No. ofgirls 2 8 12 20 8

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

Q 6

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 No. of workers 12 14 8 6 10

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

Q 7

The table below shows the daily expenditure on food of 30 households in a locality:

 Daily expenditure (in Rs) Number of households 100 – 150 6 150 – 200 7 200 – 250 12 250 – 300 3 300 – 350 2

Find the mean and median daily expenditure on food.

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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 30

Find the median of the following data by making a ‘less than ogive’.

 Marks 0 - 10 10-20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80-90 90-100 Number of Students 5 3 4 3 3 4 7 9 7 8

Q 31

The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches:

 Number of Wickets Less than 15 Less than 30 Less than 45 Less than 60 Less than 75 Less than 90 Less than 105 Less than 120 Number of bowlers 2 5 9 17 39 54 70 80

Draw a ‘less than type’ ogive from the above data. Find the median.

Q 32

Draw a ‘more than’ ogive for the data given below which gives the marks of 100 students.

 Marks 0 – 10 10 – 20 20 – 30 30 - 40 40 – 50 50 – 60 60 – 70 70 – 80 No of Students 4 6 10 10 25 22 18 5

Q 33

The heights of 50 girls of Class X of a school are recorded as follows:

 Height (in cm) 135 - 140 140 – 145 145 – 150 150 – 155 155 – 160 160 – 165 No of Students 5 8 9 12 14 2

Draw a ‘more than type’ ogive for the above data.

Q 34

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

 Monthly Consumption (in units) 140 – 160 160 – 180 180 – 200 200 – 220 220 – 240 240 – 260 260 - 280 Number of Families 3 8 15 40 50 30 10

Prepare a ‘more than type’ ogive for the given frequency distribution.

Q 35

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

 Production Yield (kg/ha) 50 –55 55 –60 60 –65 65- 70 70 – 75 75  80 Number of farms 2 8 12 24 238 16

Change the distribution to a ‘more than type’ distribution and draw its ogive. Using ogive, find the median of the given data.

Q 36

The table given below shows the weekly expenditures on food of some households in a locality

 Weekly expenditure (in Rs) Number of house holds 100 – 200 5 200- 300 6 300 – 400 11 400 – 500 13 500 – 600 5 600 – 700 4 700 – 800 3 800 – 900 2

Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

Q 37

From the following frequency, prepare the ‘more than’ ogive.

 Score Number of candidates 400 – 450 20 450 – 500 35 500 – 550 40 550 – 600 32 600 – 650 24 650 – 700 27 700 – 750 18 750 – 800 34 Total 230

Also, find the median.

Q 38

The marks obtained by 100 students of a class in an examination are given below:

 Marks Number of students 0 – 5 2 5 – 10 5 10 – 15 6 15 – 20 8 20 – 25 10 25 – 30 25 30 – 35 20 35 – 40 18 40 – 45 4 45 – 50 2

Draw cumulative frequency curves by using (i) ‘less than’ series and (ii) ‘more than’ series.Hence, find the median.

Q 39

From the following data, draw the two types of cumulative frequency curves and determine the median:

 Marks Frequency 140 – 144 3 144 – 148 9 148 – 152 24 152 – 156 31 156 – 160 42 160 – 164 64 164 – 168 75 168 – 172 82 172 – 176 86 176 – 180 34

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### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive [Page undefined]

Q 1

Write the median class of the following distribution:

 Class 0 – 10 10 -20 20- 30 30- 40 40-50 50- 60 60- 70 Frequency 4 4 8 10 12 8 4
Q 2

What is the lower limit of the modal class of the following frequency distribution?

 Age (in years) 0 - 10 10- 20 20 -30 30 – 40 40 –50 50 – 60 Number of patients 16 13 6 11 27 18
Q 3

The monthly pocket money of 50 students of a class are given in the following distribution

 Monthly pocket money (in Rs) 0 - 50 50 – 100 100 – 150 150 -200 200 – 250 250 - 300 Number of Students 2 7 8 30 12 1

Find the modal class and give class mark of the modal class.

Q 4

A data has 25 observations arranged in a descending order. Which observation represents the median?

Q 5

For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find mean for this distribution using an empirical relation.

Q 6

In a class test, 50 students obtained marks as follows:

 Marks obtained 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Number of Students 4 6 25 10 5

In a class test, 50 students obtained marks as follows:

Q 7

Find the class marks of classes 10 -25 and 35 – 55.

Q 8

While calculating the mean of a given data by the assumed-mean method, the following
values were obtained.
A=25, sum f_i d_i=110, sum f_i= 50
Find the mean.

Q 9

The distribution X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of the resulting distribution X + Y?

Q 10

In a frequency distribution table with 12 classes, the class-width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?

Q 11

The observation 29, 32, 48, 50, x, x+2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?

Q 12

The median of 19 observations is 30. Two more observation are made and the values of these are 8 and 32. Find the median of the 21 observations taken together.
Hint Since 8 is less than 30 and 32 is more than 30, so the value of median (middle value) remains unchanged.

Q 13

If the median of x/5,x/4,x/2,x and x/3, where x > 0, is 8, find the value of x.
Hint Arranging the observations in ascending order, we have x/5,x/4,x/3,x/2,x Median= x/3=8.

Q 14

What is the cumulative frequency of the modal class of the following distribution?

 Class 3 – 6 6 – 9 9 – 12 12 – 15 15 – 18 18 – 21 21 – 24 Frequency 7 13 10 23 54 21 16
Q 15

Find the mode of the given data:

 Class Interval 0 – 20 20 – 40 40 – 60 60 – 80 Frequency 15 6 18 10

Q 16

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

 Age (in years) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 -70 Number of patients 6 42 55 70 53 20

Form a ‘less than type’ cumulative frequency distribution.

Q 17

In the following data, find the values of p and q. Also, find the median class and modal class.

 Class Frequency (f) Cumulative frequency (cf) 100 – 200 11 11 200 – 300 12 p 300 – 400 10 33 400- 500 Q 46 500 – 600 20 66 600 – 700 14 80
Q 18

The following frequency distribution gives the monthly consumption of electricity of 64 consumers of locality.

 Monthly consumption (in units) 65 – 85 85 – 105 105 – 125 125 – 145 145 – 165 165 – 185 Number of consumers 4 5 13 20 14 8

Form a ‘ more than type’ cumulative frequency distribution.

Q 19

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

 Life-tine (in days) Less than50 Less than100 Less than150 Less than200 Less than250 Less than300 Number of Bulbs 7 21 52 9 91 100

Q 20

The following table, construct the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

 Marks obtained (in percent) 11 – 20 21 – 30 31 – 40 41 – 50 51 – 60 61 – 70 71 – 80 Number of Students 141 221 439 529 495 322 153

(a) Convert the given frequency distribution into the continuous form.
(b) Find the median class and write its class mark.
(c) Find the modal class and write its cumulative frequency.

Q 21

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

Q 22

Calculate the missing frequency form 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 Number ofpersons 5 25 ? 18 7

## Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive ## RS Aggarwal solutions for Secondary School Class 10 Maths chapter 9 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

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Concepts covered in Secondary School Class 10 Maths chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive are Mean of Grouped Data, Mode of Grouped Data, Median of Grouped Data, Graphical Representation of Cumulative Frequency Distribution, Ogives (Cumulative Frequency Graphs), Concepts of Statistics, Concepts of Statistics, Mean of Grouped Data, Mode of Grouped Data, Median of Grouped Data, Graphical Representation of Cumulative Frequency Distribution, Ogives (Cumulative Frequency Graphs), Concepts of Statistics, Concepts of Statistics.

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