NCERT Class 9 Maths Chapter 14 Statistics Exercise 14.4

Chapter 14 Statistics Exercise 14.4

Question 1: The following number of goals were scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Answer:

→ For mean:
Mean = Sum of all observation/Total number of observations
Mean = 2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3/10
Mean = 28/10
Mean = 2.8

→ For median:
To find median we have to arrange the given data into ascending or descending order. Therefore,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Number of observations, n = 10 (which is even)
Therefore,
Median = [n/2]th observation + [n/2 + 1]th observation/2
Median = [10/2]th observation + [10/2 + 1]th observation/2
Median = 5th observation + 6th observation/2
Median = (3 + 3)/2
Median = 3

→ For mode:
To find mode, we have to arrange the given data into ascending or descending order. Therefore,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5

After arranging the data, we see that 3 is mode of this data as it is occurring most frequently (4 times).

Question 2: In a mathematics test given to 15 students, the following marks (out of 100) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Answer:

→ For mean:
Mean = Sum of all observations/Total number of observations
Mean = 41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60/15
Mean = 822/10
Mean = 82.2

→ For median:
To find median, we have to arrange the given data in ascending or descending order. Therefore,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Number of observations, n = 15 (which is odd)
Therefore,
Median = [(n + 1)/2]th observation
Median = [15 + 1/2]th observation
Median = 8th observation or Median = 52

→ For mode:
To find mode we have to arrange the given data in ascending or descending order. Therefore,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

After arranging the data, we see that 52 is mode of this data as it is occurring most frequently (3 times).

Question 3: The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Answer:

To find the value of x, we have to first arrange the data in ascending order. Therefore,
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Number of observations = 10 (which is even)
Therefore,
Median = [n/2]th observation + [n/2 + 1]th observation/2
63 = [10/2]th observation + [10/2 + 1]th observation/2
63 = 5th observation + 6th observation/2
63 = (x + x + 2)/2
(63)2 = 2x + 2
126 = 2x + 2
124 = 2x
62 = x

Thus, the value of x is 62.

Question 4: Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
Answer:

To find the mode, we have to first arrange the given data in ascending or descending order. Therefore,
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28

After arranging the data, we see that 14 is mode of this data as it is occurring most frequently (4 times).

Question 5: Find the mean salary of 60 workers of a factory from the following table:

Salary (in ₹)

Number of workers

3000

16

4000

12

5000

10

6000

8

7000

6

8000

4

9000

3

10000

1

Total

60

Answer:

Salary (in ₹)

Number of workers (fi)

fixi

3000

16

48000

4000

12

48000

5000

10

50000

6000

8

48000

7000

6

42000

8000

4

32000

9000

3

27000

10000

1

10000

Total:

∑fi = 60

∑fixi = 305000



Question 6: Give one example of a situation in which
i) the mean is an appropriate measure of central tendency.
ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Answer:

i) Mean marks obtained in an examination.
ii) Mean is not an appropriate measure of central tendency when all the terms of the data are not fairly close to each other. Let’s take an example, we have data of the form:
50, 51, 55, 54, 200

Mean of this data is equal to 82 which is not close to any of the terms present in the data. In such a case, median is a better method. Arranging data in the ascending order we get,
50, 51, 54, 55, 200

Clearly, median of this data is equal to 54 which is close to most of the terms present in the data.

No comments:

Post a Comment

Also read!

Class 6 Solutions

• Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

• Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9 Solutions

• Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

• Computer languages
Python Basics

• Extra Activities
Extra Activities

• Extra Knowledge
Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

CONTACT US