Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

The document Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Q11. During the medical checkup of 35 students of a class, their weights were recorded as follows:

Weight (in kg)

Number of students

38-40

3

40-42

2

42-44

4

44-46

5

46-48

14

48-50

4

50-52

3

 

Draw a ‘less than type’ and ‘more than type’ ogive from the given data. Hence, obtain the median weight from the graph.

Sol.

Weight (in kg)

No. of students

Less than cumulative frequency

More than cumulative frequency

38-40

3

Less than 40 = 3

38 and more than 38 = 35

40-42

2

Less than 42 = 5

40 and more than 40 = 32

42-44

4

Less than 44 = 9

42 and more than 42 = 30

44-46

5

Less than 46 = 14

44 and more than 44 = 26

46-48

14

Less than 48 = 28

46 and more than 46 = 21

48-50

4

Less than 50 = 32

48 and more than 48 = 7

50-52

3

Less than 52 = 35

50 and more than 50 = 3

Total

∑ fi = 35

⇒ n = 35

 

 

∴ For less than type ogive, we plot the points (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32) and (52, 35).
∴ For more than type ogive, we plot the points (38, 35), (40, 32), (42, 30), (44, 26), (46, 21), (48, 7) and (50, 3) on the same graph.
From the graph, we obtain the median = 46.5 kg.

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Q12. The following table gives 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.

Sol. Let assumed mean a = 150. Here, h = 20

Daily income (in Rs)

No. of workers (fi)

xi

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

fi ui

cf

100-120

12

110

-2

-24

12 + 0 = 12

120-140

14

130

-1

-14

12 + 14 = 26

140-160

8

150

0

0

26 + 8 = 34

160-180

6

170

1

6

34 + 6 = 40

180-200

10

190

2

20

40 + 10 = 50

Total

∑ fi = 50

 

 

∑ fiui  =-12

 

 

(i) Mean  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Thus, mean income is Rs 145.2

(ii) For finding the mode,
We have the greatest frequency = 14 which lies in the class 120−140
∴ Modal class = 120−140
Therefore, l = 120
f1 = 14
f0 = 12
f2 = 8
and h = 20

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(iii) For finding median,

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

And 25 lies in the class 120−140

Median class is 120−140

Since n/2 = 25, cf = 12, f = 14 and h = 20

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

 Median income = Rs138.57

Q13. 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


Sol. Let the assumed mean a = 60. Here h = 10, we have:

Marks

obtained

Class marks

xi

fi

cf

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

fi ui

25-35

30

7

7

-3

-21

35-45

40

31

38

-2

-62

45-55

50

33

71

-1

-33

55-65

60

17

88

0

0

65-75

70

11

99

1

11

75-85

80

1

100

2

2

Total

 

∑ f = 100 ⇒ n = 100

 

 

∑ fiui =-103


(i) Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
⇒  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
(ii) Median 

Here,  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

∴ Median class is 45−55.

l = 45
cf = 38
f = 33 and h = 10

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(iii) Mode: Greatest frequency is 33 which corresponds to the class 45−55.

l = 45,  h = 10
f1 = 33,  f2 = 17
f0 = 31

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Q14. A survey regarding the heights (in cm) of 50 girls of Class X of a school was conducted and the following data was obtained:

Height (in cm)

120-130

130-140

140-150

150-160

160-170

Total

Number of girls

2

8

12

20

8

50


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

Sol. We have:

Height (in cm)

f

cf

xi

fixi

120-130

2

2 + 0 = 2

125

250

130-140

8

2 + 8 = 10

135

1080

140-150

12

10 + 12 = 22

145

1740

150-160

20

22 + 20 = 42

155

3100

160-170

8

42 + 8 = 50

165

1320

Total

50

 

 

7490

 

(i)  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(ii) ∵  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev  

∴ Median class is 150−160.
∴ We have,
l = 150
f = 20
cf = 2
2h = 10

∴  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
⇒  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(iii) ∵ Greatest frequency = 20
∴ Modal class = 150−160

So, we have

l = 150, f0 = 12, f1 = 20
f2 = 8 and h = 10

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Q15. Find the mean, mode and median of the following data:

 

Classes

Frequency

0-10

5

10-20

10

20-30

18

30-40

30

40-50

20

50-60

12

60-70

5

 
Sol. 

(i) Mean:

Let the assumed mean ‘a’ = 35

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Now we have the following data:

ClassClass mark xifiCfLong Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRevfiui

0-10

5

5

5 + 0 = 5

-3

(-3) x 5 = -15

10-20

15

10

5 + 10 = 15

-2

(-2) x 10 = -20

20-30

25

18

15 + 18 = 33

-1

(-1) x 18 = -18

30-40

35

30

33 + 30 = 63

0

0 x 30 = 0

40-50

45

20

63 + 20 = 93

1

1 x 20 = 20

50-60

55

12

83 + 12 = 95

2

2 x 12 = 24

60-70

65

5

95 + 5 = 100

3

3 x 5 = 15

 
Here ∑fi = 100 and ∑fiui = 6

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(ii) Mode:

Here, the maximum frequency is 30.
∴ Modal class is 30−40.
So, we have

l = 30, h = 10
f1 = 30,
f0 = 18
f2 = 20

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(iii) Median: 

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

∴ Median class = 30−40
So, we have:

l = 30, h = 10, cf = 33, f = 30

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Q16. Find the mean, mode and median for the following data:

Classes

Frequency

0-10

3

10-20

8

20-30

10

30-40

15

40-50

7

50-60

4

60-70

3

 

Sol. Let the assumed mean = 35;  h = 10

ClassesxificfLong Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRevfiui

0-10

5

3

3 + 0 = 3

-3

(-3) x 3 = -9

10-20

15

8

3 + 8 = 11

-2

(-2) x 8 = -16

20-30

25

10

11 + 10 = 21

-1

(-1) x 10 = -10

30-40

35

15

21 + 15 = 36

0

0 x 15 = 0

40-50

45

7

36 + 7 = 43

1

1 x 7= 7

50-60

55

4

43 + 4 = 47

2

2 x 4= 8

60-70

65

3

47 + 3 = 50

3

3 x 3= 9

Total

 

∑fi = 50

 

 

∑fiui= -11


Now,

(i)

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(ii) To find mode 
Here, highest frequency is 15.
∴ Modal class is 30−40.

Here,

l = 30, f1 = 15, f0 = 10
f2 = 7 and h = 10

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
(iii) ∵  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

So, the median class is 30−40.

∴ We have l = 30, cf = 21, f = 15 and h = 10

We have

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Q18. Find the mean, mode and median of the following data:

 

Class

Frequency

0-10

3

10-20

4

20-30

7

30-40

15

40-50

10

50-60

7

60-70

4

 

Sol. Let the assumed mean ‘a’ = 35

Here, h =10

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

ClassesxificfLong Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRevfiui

0-10

5

3

3 + 0 = 3

-3

(-3) x 3 = -9

10-20

15

4

4 + 3 = 7

-2

(-2) x 4 = -8

20-30

25

7

7 + 7 = 14

-1

(-1) x 7 = -7

30-40

35

15

15 + 14 = 29

0

0 x 15 = 0

40-50

45

10

10 + 29 = 39

1

1 x 10 = 10

50-60

55

7

7 + 39 = 46

2

2 x 7 = 14

60-70

65

4

4 + 46 = 50

3

3 x 4 = 12

Total

 

∑fi = 50

 

 

∑uifi = 12

 

(i) Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(ii) To find mode 
Here, greatest frequency = 15
∴ Modal class = 30 − 40
l = 30, f1 = 15, f0 = 7, f2 = 10 and h = 10

So, Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
⇒  Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

(iii) To find median

Here, Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
∴ Median class is 30−40.
Such that l = 30, cf = 14, f = 15 and h = 10
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev
Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 10

Dynamic Test

Content Category

Related Searches

practice quizzes

,

Important questions

,

Extra Questions

,

shortcuts and tricks

,

past year papers

,

Exam

,

Semester Notes

,

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

,

Previous Year Questions with Solutions

,

Viva Questions

,

Free

,

pdf

,

video lectures

,

ppt

,

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

,

Long Answer Type Questions(Part- 2)- Statistics Class 10 Notes | EduRev

,

mock tests for examination

,

Summary

,

study material

,

MCQs

,

Sample Paper

,

Objective type Questions

;