Solutions of chapter 9. Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and

1

If the mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find the value of x.

2

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

3

Compute the mean of the following data:

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

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

5

Calculate 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

6

Compute 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

7

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

Class interval	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?

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

9

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

Daily pocket allowance (in Rs.)	11 - 13	13 - 15	15 - 17	17 - 19	19 - 21	21 - 23	23 - 25
Number of children	7	6	9	13	F	5	4

10

If the mean of the 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

11

The mean of the following 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

12

The daily expenditure of 100 families are given below. Calculate f₁ and f₂ if the mean daily expenditure is Rs.188.

Expenditure (in Rs.)	140 - 160	160 - 180	180 - 200	200 - 220	220 - 240
Number of families	5	25	f₁	f₂	5

13

The mean of the following frequency distribution is 57.6 and the Total number of observations is 50.

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	7	f₁	12	f₂	8	5

Find f₁ and f₂.

14

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

Number of heart - beats per minute	65 - 68	68 - 71	71 - 74	74 - 77	77 - 80	80 - 83	83 - 86
Number of patients	2	4	3	8	7	4	2

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

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 of students	12	18	27	20	17	6

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

17

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

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

18

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

Literacy rate (%)	45 - 55	55 - 65	65 - 75	75 - 85	85 - 95
Number of cities	4	11	12	9	4

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

20

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

Class	5 - 15	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65	65 - 75
Frequency	6	10	16	15	24	8	7

21

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

Weight (in grams)	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.

22

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

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

23

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

Marks obtained	0 - 15	15 - 30	30 - 45	45 - 60	60 - 75	75 - 90
Number of students	2	4	5	20	9	10

Find the mean marks.

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

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

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

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
Number of cases	6	11	21	23	14	5

Find the average age of the patients.

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
Number of eggs	4	9	13	17	12	3	2

Calculate their mean weight to the nearest gram.

29

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

Marks	Less than 5	Less than 10	Less than 15	Less than 20	Less than 25	Less than 30	Less than 35	Less than 40
Number of eggs	3	10	25	49	65	73	78	80

Calculate the mean marks correct to 2 decimal places.

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
Number of patients	5	20	40	50	25

2

Compute the median 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

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.

4

Calculate the median from the following frequency distribution:

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

5

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

Consumption (in units)	65 - 85	85 - 105	105 - 125	125 - 145	145 - 165	165 - 185	185 - 205
Number of consumers	4	5	13	20	14	7	4

Calculate the median.

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
No. of boys	6	10	18	22	20	15	6	3

7

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

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

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

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 batsmen	5	X	y	12	6	2

10

If the median of the following frequency distribution is 32.5, find the values of f₁ and f₂

Class interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	Total
Number of batsmen	f₁	5	9	12	f₂	3	2	40

11

Calculate the median for the following data:

Age (in years)	19 - 25	26 - 32	33 - 39	40 - 46	47 - 53	54 - 60
Frequency	35	96	68	102	35	4

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

13

Find the median from the following data:

Class	1 - 5	6 - 10	11 - 15	16 - 20	21 - 25	26 - 30	31 - 35	36 - 40	41 - 45
Frequency	7	10	16	32	24	16	11	5	2

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

1

Find the mode of the following frequency distribution:

Marks	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Number of students	12	35	45	25	13

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

3

Heights of students of Class X are given in the following 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. Compare and interpret the two measures of central tendency.

4

Find the mode of the following distribution:

Class interval	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

5

Given below is the distribution of Total household expenditure of 200 manual workers in a city.

Expenditure (in Rs.)	No of manual workers
1000 - 1500	24
1500 - 2000	40
2000 - 2500	31
2500 - 3000	28
3000 - 3500	32
3500 - 4000	23
4000 - 4500	17
4500 - 5000	5

Find the expenditure done by maximum number of manual workers.

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

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
Number of patients	6	11	18	24	17	13	5

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

9

Compute the mode of 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

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.

1

Find the mean, mode and median of the following frequency distribution:

Class interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
Number of batsmen	4	4	7	10	12	8	5

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

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

4

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

Marks obtained	25 - 35	35 - 45	45 - 55	55 - 65	65 - 75	75 - 85
Number of students	7	31	33	17	11	1

5

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

Height (in cm)	120 - 130	130 - 140	140 - 150	150 - 160	160 - 170	Total
Total Number of girls	2	8	12	20	8	50

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

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
Number of workers	12	14	8	6	10

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

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. [CBSE 2009C]

1

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

2

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.

3

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
Number of students	4	6	10	10	25	22	18	5

4

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
Number of girls	5	8	9	12	14	2

Draw a 'more than type' ogive for the above data.

5

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.

6

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	14	24	38	16

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

7

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

Weekly expenditure (in Rs.)	Number of households
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.

8

From the following frequency distribution, 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.

9

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.

10

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

Height (in cm)	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

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

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
60 Number of patients	16	13	6	11	27	18

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 also give class mark of the modal class.

4

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

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.

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

Find the modal class and the median class.

7

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

8

While calculating the mean of a given data by the Assumed - mean method, the following values were obtained:

A = 25, = 110, = 50.

Find the mean.

9

The distributions 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?

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?

11

The observations 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?

12

The median of 19 observations is 30. Two more observations are made and the values of these are 8 and 32. Find the median of the 21 observations taken together.

13

If the median of and , where x > 0, is 8, find the value of x.

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	4	21	16

15

Find the mode of the given data:

Class interval	0 - 20	20 - 40	40 - 60	60 - 80
Frequency	15	6	18	10

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	60	42	55	70	53	20

Form a 'less than type' cumulative frequency distribution.

17

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

Class	Frequency (f)	cummulative 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

18

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

19

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

Life - time (in days)	Less than 50	Less than 100	Less than 150	Less than 200	Less than 250	Less than 300
Number of bulbs	7	21	52	79	91	100

From this table, construct the frequency distribution table.

20

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

Marks obtained (in per cent)	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.

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

22

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
Number of persons	5	25	?	18	7

1

Which of the following is not a measure of central tendency?

2

Which of the following cannot be determined graphically?

3

Which of the following measures of central tendency is influenced by extreme values?

4

The mode of a frequency distribution is obtained graphically from

5

The median of a frequency distribution is found graphically with the help of

6

The cumulative frequency table is useful in determining the

7

The abscissa of the point of intersection of the Less Than Type and of the More Than Type cumulative frequency curves of a grouped data gives its

8

If x_i's are the midpoints of the class intervals of a grouped data, f_i's are the corresponding frequencies and 7 is the mean then

9

For finding the mean by using the formula, , we have u_i = ?

10

In the formula, for finding the mean of the grouped data, the d_i's are the deviations from A of

11

While computing the mean of the grouped data, we Assume that the frequencies are

12

The relation between mean, mode and median is

13

If the 'less than type' ogive and 'more than type' ogive intersect each other at (20.5, 15.5) then the median of the given data is

14

Consider the frequency distribution of the heights of 60 students of a class:

Height (in cm)	No of Students	Cumulative Frequency
150 - 155	16	16
155 - 160	12	28
160 - 165	9	37
165 - 170	7	44
170 - 175	10	54
175 - 180	6	60

The Sum of the lower limit of the modal class and the upper limit of the median class is

15

Consider the following frequency distribution:

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	3	9	15	30	18	5

The modal class is

16

Mode = ?

17

Median = ?

18

If the mean and median of a set of numbers are 8.9 and 9 respectively then the mode will be

19

Look at the frequency distribution table given below:

Class interval	35 - 45	45 - 55	55 - 65	65 - 75
Frequency	8	12	20	10

The median of the above distribution is

20

Consider the following table:

Class interval	10 - 14	14 - 18	18 - 22	22 - 26	26 - 30
Frequency	5	11	16	25	19

The mode of the above data is

21

The mean and mode of a frequency distribution are 28 and 16 respectively. The median is

22

The median and mode of a frequency distribution are 26 and 29 respectively. Then, the mean is

23

For a symmetrical frequency distribution, we have

24

Look at the cumulative frequency distribution table given below:

Monthly income	Number of families
More than Rs. 10000	100
More than Rs. 14000	85
More than Rs. 18000	69
More than Rs.20000	50
More than Rs. 25000	37
More than Rs. 30000	15

Number of families having income range 20000 to 25000 is

25

The median of first 8 prime numbers is

26

The mean of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

27

If the median of the data 4,7,x - 1,X - 3,l6,25, written in ascending order, is 13 then x is equal to

28

The mean of 2, 7, 6 and x is 15 and the mean of 18, 1, 6, x and y is 10. What is the value of y?

29

Match the following columns:

Column I	Column II
(a) The most frequent value in a data is known as …….	(p) standard deviation
(b) Which of the following cannot be determined graphically out of mean, mode and median?	(q) median
(c) An ogive is used to determine …….	(r) mean
(d) Out of mean, mode, median and standard deviation, which is not a measure of central tendency?	(s) mode

The correct answer is:

30

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A)	Reason (R)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.	Mean, median and mode of a frequency distribution are related as: mode = 3 median - 2 mean.

31

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A)

Reason (R)

Consider the following frequency distribution:

Class interval	3 - 6	6 - 9	9 - 12	12 - 15	15 - 18	18 - 21
Frequency	2	5	21	23	10	12

The mode of the above data is 12.4.

The value of the variable which occurs most often is the mode.

1

Which one of the following measures is determined only after the construction of cumulative frequency distribution?

2

If the mean of a data is 27 and its median is 33 then the mode is

3

Consider the following distribution:

Class interval	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25
Frequency	10	15	12	20	9

The Sum of the lower limits of the median class and the modal class is

4

Consider the following frequency distribution:

Class interval	0 - 5	6 - 11	12 - 17	18 - 23	24 - 29
Frequency	13	10	15	8	11

The upper limit of the median class is

5

If the mean and mode of a frequency distribution be 53.4 and 55.2 respectively, find the median.

6

In the table given below, the times taken by 120 athletes to run a 100 - m - hurdle race are given.

Class	13.8 - 14	14 - 14.2	14.2 - 14.4	14.4 - 14.6	14.6 - 14.8	14.8 - 15
Frequency	2	4	15	54	25	20

Find the number of athletes who completed the race in less than 14.6 seconds.

7

Consider the following frequency distribution:

Class	0 - 5	6 - 11	12 - 17	18 - 23	24 - 29
Frequency	13	10	15	8	11

Find the upper limit of the median class.

8

The annual profits earned by 30 shops of a shopping complex in a locality are recorded in the table shown below:

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

If we draw the frequency distribution table for the above data, find the frequency corresponding to the class 20 - 25.

9

Find the mean of the following frequency distribution:

Class	1 - 3	3 - 5	5 - 7	7 - 9
Frequency	9	22	27	18

10

The maximum bowling speeds (in km/hr) of 33 players at a cricket coaching centre are given below:

Speed in km/hr	85 - 100	100 - 115	115 - 130	130 - 145
No. of players	10	4	7	9

Calculate the median bowling speed.

11

The arithmetic mean of the following frequency distribution is 50.

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Frequency	16	p	30	32	14

Find the value of p.

12

Find the median of the following frequency distribution:

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Number of students	6	16	30	9	4

13

Following is the distribution of marks of 70 students in a periodical test:

Marks	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50
Number of students	3	11	28	48	70

Draw a cumulative frequency curve for the above data.

14

Find the median of the following data.

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	Total
Number of students	8	16	36	34	6	100

15

For the following distribution draw a 'less than type' ogive and from the curve find the median.

Marks obtained	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80	Less than 90	Less than 100
Number of students	2	7	17	40	60	82	85	90	100

16

The median value for the following frequency distribution is 35 and the Sum of all the frequencies is 170. Using the formula for median, find the missing frequencies.

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

17

Find the missing frequencies f₁ and f₂ in the table given below, it being given that the mean of the given frequency distribution is 50.

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	Total
Total Frequency	17	f₁	32	f₂	19	120

18

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

Class	84 - 90	90 - 96	96 - 102	102 - 108	108 - 114	114 - 120
Frequency	15	22	20	18	20	25

19

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	6	8	10	15	5	4	2

20

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data:

Class	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
Frequency	2	12	2	4	3	4	3

21

The production yield per hectare of wheat of some farms of a village are given in the following table:

Production yield (in kg/ha)	40 - 45	45 - 50	50 - 55	55 - 60	60 - 65	65 - 70	70 - 75	75 - 80	80 - 85
Number of farms	1	9	15	18	40	26	16	14	10

Draw a less than type ogive and a more than type ogive for this data.

22

The following table gives the marks obtained by 50 students in a class test:

Marks	11 - 15	16 - 20	21 - 25	26 - 30	31 - 35	36 - 40	41 - 45	46 - 50
Number of students	2	3	6	4	14	12	4	2

Calculate the mean, median and mode for the above data.

Book: RS Aggarwal - Mathematics

Chapter: 9. Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and

Subject: Maths - Class 10^th

Chapter Exercises

Exercise 9A

Exercise 9B

Exercise 9C

Exercise 9D

Exercise 9E

Exercise 9F

Multiple Choice Questions (MCQ)

Formative Assessment (Unit Test)

Exercise 9A

Exercise 9B

Exercise 9C

Exercise 9D

Exercise 9E

Exercise 9F

Multiple Choice Questions (MCQ)

Formative Assessment (Unit Test)

Premium Lectures

Book: RS Aggarwal - Mathematics

Chapter: 9. Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and

Subject: Maths - Class 10th

Chapter Exercises

Exercise 9A

Exercise 9B

Exercise 9C

Exercise 9D

Exercise 9E

Exercise 9F

Multiple Choice Questions (MCQ)

Formative Assessment (Unit Test)

Subject: Maths - Class 10^th