NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Long Answer

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Question

The lengths of 50 leaves of a plant are measured correct to the nearest millimeter and the data obtained is represented in the following table

The nearest millimeter and the data obtained is represented

Length (in mm)

109-117

118-126

127-135

136-144

145-153

154-162

163-171

No. of leaves

4

6

14

13

6

4

3

Find the mean length of the leaves.

Solution

The nearest millimeter and the data obtained is represented

Class Interval

108.5-117.5

117.5-126.5

126.5-135.5

135.5-144.5

144.5-153.5

153.5-162.5

162.5-171.5

113

122

131

140

149

158

167

4

6

14

13

6

4

3

-3

-2

-1

0

1

2

3

-12

-12

-14

0

6

8

9

Total

Given frequency distribution is not continuous. So first we have to make it continuous.

Here assumed mean (a) =140; class size =9

Now,

Hence, mean length of the leaves -137.30mm.

Question

Draw a ‘less than type’ ogive for the following frequency distribution.

Draw a ‘less than type’ ogive

Class

15-20

20-25

25-30

30-35

35-40

40-45

Frequency

13

18

31

25

15

5

Solution

Draw a ‘less than type’ ogive

Draw a ‘Less Than Type’ Ogive

Loading image
Draw a ‘less than type’ ogive

Class

Frequency

Less than 20

Less than 25

Less than 30

Less than 35

Less than 40

Less than 45

13

Question

In a retail market, fruit vendor were selling mangoes in packing boxes. These boxes contained varying number or mangoes. The following was the distribution.

In a retail market, fruit vendor were selling mangoes in packing boxes.

No. of mangoes

50-52

53-55

56-58

59-61

62-64

No. of boxes

15

110

135

115

25

Find the mean and median number of mangoes kept in a packing box.

Solution

In a retail market, fruit vendor were selling mangoes in packing boxes.

Class interval

Mid value ()

(where a=57)

49.5-52.5

52.5-55.5

55.5-58.5

58.5-61.5

61.5-64.5

51

54

57=a

60

63

-2

-1

0

1

2

15

110

135

115

25

-30

-110

0

115

50

15

125

260

375

400

Mean

For median: Median

Here

Median class is 55.5-58.5

Median

Question

The following table gives production yield of rice per hectare in some farms of a village:

Production yield (in kg/hectare)

Production yield (in kg/hectare)

10-20

20-30

30-40

40-50

50-60

No. of farms

3

9

12

20

6

Draw a more than type’ ogive. Also, find median from the curve.

Solution

Production yield (in kg/hectare)

Production yield (in kg/hectare)

Class interval

Frequency

Production yield more than or eual to

10-20

20-30

30-40

40-50

50-60

3

9

12

20

6

10

20

30

40

50

50

47

38

26

6

Frequency

Frequency

Loading image

Question

Draw a more than type ogive and from it find median

Life time (in hours)

More than or equal to 240

More than or equal to 280

More than or equal to 320

More than or equal to 360

More than or equal to 400

More than or equal to 440

More than or equal to 480

Number of bulbs

100

95

87

77

47

22

10

Draw a more than type ogive and from it find median. Verify it by actual calculations.

Solution

Draw a more than type ogive and from it find median

More than or equal to

Number of bulbs

240

280

320

360

400

440

480

100

95

87

77

47

22

10

Draw a more than type ogive and from it find median

Draw a More Than Type Ogive and from It Find Median

Loading image

Median from curve is 396.

Median from curve is 396

Class interval

Frequency

Cumulative frequency

240-280

280-320

320-360

360-400

400-440

440-480

480-520

5

8

10

30

25

12

10

5

13

23

53

78

90

100

Median class

100

Median

Question

Change the following distribution to a ‘more than type’ distribution. Hence draw the ‘more than type’ ogive for this distribution.

Change the following distribution to a ‘more than type’ distribution

Class Interval

20-30

30-40

40-50

50-60

60-70

70-80

80-90

Frequency

10

8

12

24

6

25

15

Solution

Class Interval Cumulative Frequency

Class Interval

Cumulative Frequency

More than or equal to 20

100

More than or equal to 30

90

More than or equal to 40

82

More than or equal to 50

70

More than or equal to 60

46

More than or equal to 70

40

More than or equal to 80

15

Plot of points (20. 100), (30. 90), (40, 82), (50. 70), (60,46), (70. 40) and (80. 15)

Join the points to get a curve

Question

The mean of the following distribution is 18. Find the frequency f of the class 19 —21.

Find the frequency f of the class 19 —21

Class

11-13

13-15

15-17

17-19

19-21

21-23

23-25

Frequency

3

6

9

13

f

5

4

Solution

Find the frequency f of the class 19 —21

Class

x

f

11-13

12

3

36

13-15

14

6

84

15-17

16

9

144

17-19

18

13

234

19-21

20

f

20f

21-23

22

5

110

23-25

24

4

96

Mean

Question

If the median of the following frequency distribution is 32.5. Find the values of and .

If the median of the following frequency distribution is 32

Class

0-10

10-20

20-30

30-40

40-50

50-60

70-80

Total

Frequency

5

9

12

3

2

40

Solution

ClassFrequency Cumulative Frequency

Class

Frequency

Cumulative Frequency

0-10

10-20

5

20-30

9

30-40

12

40-50

50-60

3

60-70

2

40

Median median class is 30-40.

Now

Also,

Question

The following distribution gives the daily income of 50 workers of a factory

Daily income of 50 workers of a factory

Daily Income

400-420

400-420

400-420

400-420

400-420

Number of workers

12

12

12

12

12

Convert this distribution to less than a type of cumulative frequency distribution and draw its ogive.

Solution

Daily Income Number of workers Cumulative Frequen

Daily Income

Number of workers

Cumulative Frequency

400-420

12

12

420-440

14

26

440-460

8

34

460-480

6

40

480-500

10

50

Correct Table

Drawing an ogive with coordinates

Question

Calculate Mean of the following distribution

Calculate Mean of the following distribution

C.I

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

Frequency

5

9

13

17

16

11

12

9

8

Solution

Calculate Mean of the following distribution

10-19

14.5

5

-40

-4

20

20-29

24.5

9

-30

-3

-27

30-39

34.5

13

-20

-2

-26

50-50

44.5

17

-10

-1

-17

40-49

54.5

16

0

0

0

60-69

64.5

11

10

1

11

70-79

74.5

12

20

2

24

80-89

84.5

9

30

3

27

90-99

94.5

8

40

4

32

100

Question

If the mean of x and is M, find the mean of and

Solution

Mean of and is