Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Class 9 Mathematics by Full Circle

Created by: Full Circle

Class 9 : Short Answers Type Questions- Statistics Class 9 Notes | EduRev

The document Short Answers Type Questions- Statistics Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.
All you need of Class 9 at this link: Class 9

Question 1. Find the mean of: 10, 90, 20, 80, 30 and 70.
 Solution:
Number of observations = 6 Sum of the observations = 10 + 90 + 20 + 80 + 30 + 70 = 300
∴ Mean = (300/6)= 50
Thus, the required mean = 50


Question 2. Find the range and prepare a frequency table for the following observations:
 4, 1, 1, 2, 3, 5, 2, 3, 3, 1, 2, 2, 4, 2, 5, 4, 1, 1, 3, 2
 Solution:
Arranging the observations in an ascending order:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5
Lowest observation = 1
Highest observation = 5

∴ Range = 5 – 1 = 4
Thus, the required range = 4.
Frequency table:

Observation

Tally marks

Frequency

1

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

5

2

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

6

3

IIII

4

4

III

3

5

II

2


Question 3. Make a cumulative frequency table for the following:

 

Class interval

Tally marks

Frequency

100-110

IIII

4

110-120

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

6

120-130

II

2

130-140

III

3

140-150

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

5

Total

20

 

Solution: Cumulative frequency table:

Class interval

Tally marks

Frequency

Cumulative frequency

100-110

IIII

4

4

110-120

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

6

6 + 4 = 10

120-130

II

2

10 + 2 = 12

130-140

III

3

12 + 3 = 15

140-150

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

5

15 + 5 = 20

Total

20

 

Question 4. Form a frequency table for the following:

Marks obtained Number of students 
More than 50
More than 40
More than 30
More than 20
More than 10
More than 0  
0
20
37
44
46
50

Solution:

Marks obtainedFrequencyCumulative frequency
0–10
10–20  
20–30
30–40  
40–50
50 – 46 = 4  
46 – 44 = 2 
44 – 37 = 7 
37 – 20 = 17 
20 – 0 = 20  
4
6
13
30
50
Total50 

 

Question 5. Find the mean of the first six multiples of 6.
 Solution:
Six multiples of 6 are: 6, 12, 18, 24, 30, 36

Short Answers Type Questions- Statistics Class 9 Notes | EduRev
Thus, the required mean = 21


Question 6. If the mean of 8, 5, 2, x, 6, 5 is 6, then find the value of x.
 Solution:
We have the number of observations = 6

∴               Mean = Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Now,        Short Answers Type Questions- Statistics Class 9 Notes | EduRev             [∵ Mean is 6]

⇒ 26 + x = 6 x 6 ⇒ x = 36 – 26 = 10


 Question 7. If the mean of the following data is 15 then find the value of p.

xi510152025
fi645p7

Solution: We can have the following table from the given data :

Short Answers Type Questions- Statistics Class 9 Notes | EduRev   

∴ we have           ∑ (fi) = 6+4+5+p+7 = 22+p

                           ∑ (xifi) = 30+40+75+20p+175 = 320+20p

∵ Mean,               Short Answers Type Questions- Statistics Class 9 Notes | EduRev

 But Mean = 15

∴    Short Answers Type Questions- Statistics Class 9 Notes | EduRev

 ⇒ 320 + 20p = 15(22 + p)
⇒ 320 + 20p = 330 + 15p
⇒ 20p – 15p = 330 – 320
⇒ 5p = 10
⇒   p= (10/5)= 2
Thus, the required value of p is 2

 

Question 8. If the mean of the following data is 18.75, find the value of p:

xi101520p30
fi510782

Solution: From the given data we can prepare the following table:

xi

fi

(fi * xi)

10

5

10 x 5 = 50

15

10

15 x 10 = 150

20

7

20 x 7 = 140

P

S

p x 8 = 8p

30

2

30 x 2 = 60

 

∑(fi) = 32

∑(xi * fi) = 400 + 8p

 

∵     Short Answers Type Questions- Statistics Class 9 Notes | EduRev

But mean is 18.75.

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

⇒ 400 + 8p = 18.75 x 32
⇒ 400 + 8p = 600
⇒ 8p = 600 – 400 = 200
⇒   p= (200/8) = 25
Thus, the required value of p is 25.


Question 9. The following observations are arranged in ascending order:
 26,  29,  42,  53,  x,  x + 2,  70,  75,  82,  93
 If the median is 65, find the value of x.
 Solution:
Number of observations (n) = 10 Here ‘n’ is even

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

∴ x + 1 = 65 or x = 65 – 1 = 64

Thus, the required value of x is 64.

 

Question 1. Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 30 workers of a factory taking one of the class interval as
 8440–8540 (8540 not included). 8740, 8780, 8760, 8740, 8450, 8200, 8440, 9080, 8880, 8840, 8340, 8140, 8660, 8960, 8400, 9100,
 8460, 8880, 8540, 8140, 8760, 8300, 8350, 8660, 8950, 9120, 9100, 8320, 8150, 9080.
 Solution: 
Here, the lowest observation = 8140
The highest observation = 9120
∵ One of the classes is 8440–8540,
i.e. the class size = 100
∴ To cover the given data, we have the classes as: 8140–8240; 8240–8340; ….; 9040–9140.
Now, the required frequency table is:

Wages (in f)

Tally marks

Frequency

8140-8240

IIII

4

8240-8340

II

2

8340-8440

III

3

8440-8540

III

3

8540-8640

I

1

8640-8740

II

2

8740-8840

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

5

8840-8940

III

3

8940-9040

III

3

9040-9140

IIII

4

Total

30

Question 2. The mean of 40 numbers was found to be 35. Later on it was detected that a number 56 was misread as 16. Find the correct mean of the given numbers.
 Solution: 
Number of observations = 40
∵ Calculated mean = 35
∴ Calculated sum = 40 x 35 = 1400
Since the number 56 is misread as 16.
∴ Correct sum of the numbers = 1400 – [Wrong observation] + [Correct observation]
= 1400 – [16] + [56]
= (1400 – 16 + 56) = 1440
∴ The correct mean =Short Answers Type Questions- Statistics Class 9 Notes | EduRev

= (14440/40)= 36
Thus, the correct mean = 36.

 

Question 3. The mean of 72 items was found to be 63. If two of the items were misread as 27 and 9 instead of 72 and 90 respectively. Find the correct mean.
 Solution:
Number of items = 72
Calculated mean = 63
∴ Calculated sum = 72 x 63 = 4536
Since, the item 72 is misread as 27.
And the item 90 is misread as 9.
∴ Correct sum of 72 items = [Calculated sum] – [Sum of the wrong items] + [Sum of the correct items]
= [4536] – [27 + 9] + [72 + 90] = [4536] – [36] + [162]
= [4536 – 36 + 162] = 4662
∴ Correct mean Short Answers Type Questions- Statistics Class 9 Notes | EduRev

 

Thus, the required correct mean is 64.75.
 

Question 4. A train travels between two stations x and y. While going from x to y, its average speed is 72 km per hour, and while coming back from y to x, its average speed is 63 km per hour. Find the average speed of the train during the whole journey.
 Solution: 
Let the distance between x and y is s km.
Since, average speed = Total Distance / Total Time

For the train going from x to y, Average speed = 72 km/hr
∴ Time taken = Distance / speed = s/72 hours

For the train coming back from y to x, Average speed = 63 km/hr
∴ Time taken = Distance / speed = s/63 hours

 Now, total time taken to cover 2s km

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

∴ Average speed during the whole journey Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Thus, the required average speed = 67.2 km/hr.

 

 Question 5. Find the mode for the following data using the relation : mode = (3 median – 2 mean)

Item (x) Frequency (f) 
16 
17 
18 
19 
20 
21 
1
1
3
4
1
2

 

Item (x)Frequency (f)Cumulative frequencyf-x

16

17

18

19

20

21

1

1

3

4

1

2

1

2

5

9

10

12

16

17

54

76

20

42

Total  225


Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

Since, Mode = 3(Median) – 2(Mean)
∴ Mode of the above data = 3(19) – 2(18.75)
= 57 – 37.5 = 19.5

Share with a friend

Complete Syllabus of Class 9

Dynamic Test

Content Category

Related Searches

Summary

,

Sample Paper

,

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

,

MCQs

,

mock tests for examination

,

Objective type Questions

,

shortcuts and tricks

,

Semester Notes

,

Exam

,

Free

,

Previous Year Questions with Solutions

,

study material

,

practice quizzes

,

video lectures

,

ppt

,

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

,

Viva Questions

,

pdf

,

Short Answers Type Questions- Statistics Class 9 Notes | EduRev

,

Extra Questions

,

past year papers

,

Important questions

;