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Page No 193:

Question 1:

The table below classifies the number of days of a month according to the amount of rainfall received in a certain locality.

Find the mean daily rainfall during this month.

Rainfall

(mm)

 

Number of days

 

54

56

58

55

50

47

44

41

 

3

5

6

3

2

4

5

2

 

Answer:

We can make the complete table as follows:

Rainfall 

(mm)

 

Number of Days

 

Total Rainfall (mm)

 

54

 

3

 

162

 

56

 

5

 

280

 

58

 

6

 

348

 

55

 

3

 

165

 

50

 

2

 

100

 

47

 

4

 

188

 

44

 

5

 

220

 

41

 

2

 

82

 

Total

 

30

 

1545

 


 

Mean daily rainfall =



Page No 194:

Question 1:

The table below classifies the members of a committee according to their ages.

Age

 

Number of Members

 

25 − 30

30 − 35

35 − 40

40 − 45

45 − 50

50 − 55

55 − 60

 

6

14

16

22

5

4

3

 

Calculate the mean age of the members of this committee.

Answer:

We can make the complete table as follows:

Age

 

Number of Member

 

Class Average

 

Total Age

 

25 − 30

 

6

 

27.5

 

165

 

30 − 35

 

14

 

32.5

 

455

 

35 − 40

 

16

 

37.5

 

600

 

40 − 45

 

22

 

42.5

 

935

 

45 − 50

 

5

 

47.5

 

237.5

 

50 − 55

 

4

 

52.5

 

210

 

55 − 60

 

3

 

57.5

 

172.5

 

Total

 

70

 

 

 

2775

 


 

Mean age of the members of the committee =

Page No 194:

Question 2:

The table below shows the number of students in class 10 of a school, classified according to their heights:

Height

(cm)

 

Number of Students

 

120 − 125

125 − 130

130 − 135

135 − 140

140 − 145

145 − 150

150 − 155

155 − 160

 

19

36

23

23

43

21

23

12

 

Calculate the mean height

Answer:

We can make the complete table as follows:


 

Height 

(cm)

 

Number of Student

 

Class Average

 

Total Height

 

120 − 125

 

19

 

122.5

 

2327.5

 

125 − 130

 

36

 

127.5

 

4590.0

 

130 − 135

 

23

 

132.5

 

3047.5

 

135 − 140

 

23

 

137.5

 

3162.5

 

140 − 145

 

43

 

142.5

 

6127.5

 

145 − 150

 

21

 

147.5

 

3097.5

 

150 − 155

 

23

 

152.5

 

3507.5

 

155 − 160

 

12

 

157.5

 

1890.0

 

Total

 

200

 

 

 

27750

 


 

Mean height =



Page No 199:

Question 1:

The table below classifies according to weight, the infants born during a week in a hospital:

Weight

(kg)

 

Number of Infants

 

2,500

2,600

2,750

2,800

3,000

3,150

3,250

3,300

3,500

 

4

6

8

10

12

10

8

7

5

 

Find the median weight.

Answer:

The given data can be shown as:

Weight 

(kg)

 

Number of Infant

 

Up to 2.500

 

4

 

Up to 2.600

 

10

 

Up to 2.750

 

18

 

Up to 2.800

 

28

 

Up to 3.000

 

40

 

Up to 3.150

 

50

 

Up to 3.250

 

58

 

Up to 3.300

 

65

 

Up to 3.500

 

70

 


 

Here, we need to find the weight of infant. 

From the table it can be inferred that the weight of the 29th infant to the 40th infant is 3.000 kg.

So, the weight of the 35th infant is 3.000 kg.

Thus, the median weight of the infants born during the week in the hospital is 3.000 kg.



Page No 200:

Question 1:

The table below shows the number of employees of an office, classified according to the income-tax paid by them.

Income Tax

(Rupees)

 

Number of Employees

 

1000 − 2000

2000 − 3000

3000 − 4000

4000 − 5000

5000 − 6000

6000 − 7000

7000 − 8000

8000 − 9000

 

8

10

15

18

22

8

6

3

 

Compute the median income-tax.

Answer:

The given data can be shown as:

Income Tax (Rupees)

 

Number of Employee

 

Below 2000

 

8

 

Below 3000

 

18

 

Below 4000

 

33

 

Below 5000

 

51

 

Below 6000

 

73

 

Below 7000

 

81

 

Below 8000

 

87

 

Below 9000

 

90

 


 

Let us tabulate the numbers 2000, 3000, … in the first row and 8, 18, … in the second row.

x

 

2000

 

3000

 

4000

 

5000

 

6000

 

7000

 

8000

 

9000

 

y

 

8

 

18

 

33

 

51

 

73

 

81

 

87

 

90

 


 

We know that the change in y is proportional to the corresponding change in x.

We have to find that value of x for which y =

The number 45 is between the numbers y = 33 and y = 51.

The corresponding numbers are x = 4000 and x = 5000.

Thus, we must have:

Thus, the median income tax of the employees of the office is Rs.4666.67.

Page No 200:

Question 2:

The table below classifies the candidates who took and examination, according to the marks scored by them:

Marks

 

Number of Candidates

 

0 − 10

10 − 20

20 − 30

30 − 40

40 − 50

50 − 60

60 − 70

70 − 80

80 − 90

90 − 100

 

44

40

35

20

12

10

8

6

4

1

 

Find the median mark.

Answer:

Given data can be shown as:

Marks

 

Number of candidate

 

Below 10

 

44

 

Below 20

 

84

 

Below 30

 

119

 

Below 40

 

139

 

Below 50

 

151

 

Below 60

 

161

 

Below 70

 

169

 

Below 80

 

175

 

Below 90

 

179

 

Below 100

 

180

 


 

Let us tabulate the numbers 10, 20, … in the first row and 44, 84, … in the second row.

x

 

10

 

20

 

30

 

40

 

50

 

60

 

70

 

80

 

90

 

100

 

y

 

44

 

84

 

119

 

139

 

151

 

161

 

169

 

175

 

179

 

180

 


 

We know that the change in y is proportional to the corresponding change in x.

We have to find that value of x for which y =

The number 90 is between the numbers y = 84 and y = 119.

The corresponding numbers are x = 20 and x = 30.

Thus, we must have:

Thus, the median marks of the candidates who took an examination is 21.71.



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