RD Sharma Solutions Chapter 7 Statistics Exercise 7.5 Class 10 Maths

RD Sharma Solutions Chapter 7 Statistics Exercise 7.5 Class 10 Maths

Chapter Name

RD Sharma Chapter 7 Statistics

Book Name

RD Sharma Mathematics for Class 10

Other Exercises

  • Exercise 7.1
  • Exercise 7.2
  • Exercise 7.3
  • Exercise 7.4
  • Exercise 7.6

Related Study

NCERT Solutions for Class 10 Maths

Exercise 7.5 Solutions

1. Find the mode of the following data:
(i) 3,5,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4
(ii) 3,3,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4
(iii) 15,8,26,25,24,15,18,20,24,15,19,15

Solution


2. 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.

Solution

Shirt size:

37

38

39

40

41

42

43

44

Frequency (f)

15

25

39

41

36

17

15

12

Model shirt size = 40 because it occurs maximum number of times


3. Find the mode of the following distribution.

(i)

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

(ii)

Class – inteval:

10 – 15

15 – 20

20 – 25

25 – 30

30 – 35

35 – 40

Frequency:

30

45

75

35

25

15

(iii)

Class – interval:

25 – 30

30 – 35

35 – 40

40 – 45

45 – 50

50 – 60

Frequency:

25

34

50

42

38

14

Solution


4. 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

Solution


= 18.83
Hence the mode of age for the group A is higher than group B.

5. 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

Solution


6. 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.

Solution


7. 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

No. of students:

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.

Solution


8. 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

No. of components:

10

35

52

61

38

29

Determine the modal lifetimes of the components.

Solution
From data as given above we may observe that maximum class frequency 61 belonging to 
class interval 60 - 80. 
So, modal class 60 - 80 


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

Expenditure (in Rs.)

Frequency

Expenditure(in Rs.)

Frequency

1000 – 1500

24

3000 – 3500

30

1500 – 2000

40

3500 – 4000

22

2000 – 2500

33

4000 – 4500

16

2500 – 3000

28

4500 – 5000

7

Solution



10. 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.

Number of students per teacher

Number of states/U.T.

15 – 20

3

35 – 40

3

20 – 25

8

40 – 45

0

25 – 30

9

45 – 50

0

30 – 35

10

50 – 55

2

Solution


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

Runs scored

No. of batsman

Runs scored

No. of batsman

3000 – 4000

4

7000 – 8000

6

4000 – 5000

18

8000 – 9000

3

5000 – 6000

9

9000 – 10000

1

6000 – 7000

7

10000 – 11000

1

Find the mode of the data.

Solution

From the given data we may observe that maximum class frequently is 18 belonging to 
class interval  4000 - 5000
So modal class 4000 - 5000 
Lower limit(1) of model class = 4000


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

Solution

From the given data we may observe that maximum class internal frequency is 200 belonging to modal class = 40 - 50 


13. 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 the compare them.

Monthly consumption(in units)

65 – 85

85 – 105

105 – 125

125 – 145

145 – 165

165 – 185

185 – 205

No. of consumers:

4

5

13

20

14

8

4

Solution


14. 100 surnames were randomly picked up from a local telepone directly and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters:

1 – 4

4 – 7

7 – 10

10 – 13

13 – 16

16 – 19

Number surnames:

6

30

40

16

4

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.

Solution


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

Classes:

0 – 20

20 – 40

40 – 60

60 – 80

80 – 100

100 – 120

120 – 140

Frequency:

6

8

10

12

6

5

3

Solution


16. 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

Solution


17. 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.

Solution

Previous Post Next Post