Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Class 9 Mathematics by Full Circle

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Class 9 : Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

The document Ex 14.4 NCERT Solutions- 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. 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.
 Solution: 
To find mean: Here, n = 10,

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

= (28/10) = 2.8
∴ Mean = 2.8
To find median:
Arranging the given data in an ascending order, we have: 0, 1, 2, 3, 3, 3, 3, 4, 4, 5
For even observation, we have median Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Thus, the median of the data = 3
To find the mode:
∵ In the given data 0 occurs 1 time, 1 occurs 1 time, 2 occurs 1 time, 3 occurs 4 times, 4 occurs 2 times, 5 occurs 1 time
∵ 3 occurs maximum number of times.
∴ Mode = 3.


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.
 Solution: 
To find the mean:

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

=(822/15) = 54.8
Thus, mean = 54.8
To find median:
Arranging the given data in an ascending order, we have:
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
∵ n = 15, an odd number

∴   Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

 = (16/2)th term = 8th term = 52

Thus, the median = 52
To find mode:
∵ In the given data, the observation 52 occurs 3 times, i.e., the maximum number of times.
∴ Mode = 52


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
 Solution: 
Here, the given observations are in an ascending order.
∵ n = 10 (an even number of observations)

∴   Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Since, median = 63                   [Given]
∴ x + 1 = 63
⇒   x = 63 – 1 = 62
Thus, the required value of x is 62.

 

Question 4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
 Solution:
Arranging the given data in an ascending order: 14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.
∴ The observation 14 is occurring the maximum number of times (i.e., 4 times)
∴ Mode of the given data = 14


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

Salary in ₹Number of workers
300016
400012
500010
60008
70006
80004
90003
100001
Total60

Solution: Let salaries be represented by xi and number of corresponding workers by fi.
Note: The mean x of n observations having values as x1, x2, x3, …, xand occurring with frequencies f1, f2, f3, …, fn respectively is given by

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Here,
fx x1 = 16 x 3000 = 48,000
f2 x x2 = 12 x 4000 = 48,000
f3 x x3 = 10 x 5000 = 50,000
fx x4 = 8 x 6000 = 48,000
f5 x x5 = 6 x 7000 = 42,000
f6 x x= 4 x 8000 = 32,000
f7 x x= 3 x 9000 = 27,000
f8 x x8 = 1 x 10000 = 10,000

∴  Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev = [48000 + 48000 + 50000 + 48000 + 42000 + 32000 + 27000 + 10000]
= 305000

and Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev = 16 + 12 + 10 + 8 + 6 + 4 + 3 + 1 = 60

⇒          Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Thus, the mean salary = ₹ 5080.33

salary in ₹ (xi)number of workers (fi)(fi xi)
30001616 x 3000 = 48000
40001212 x 4000 = 48000
50001010 x 5000 = 50000
600088 x 6000 = 48000
700066 x 7000 = 42000
800044 x 8000 = 32000
900033 x 9000 = 27000
1000011 x 10000 = 10000
TotalEx 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRevEx 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

 

Ex 14.4 NCERT Solutions- Statistics Class 9 Notes | EduRev

Thus, the required mean salary = ₹ 5080.33


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.

Solution: (i) Mean is a quantitative central tendency of a data.
Example: For measuring central tendency of marks of a test we find the mean of the data.
(ii) Median is a qualitative central tendency of a data.
Example: For measuring central tendency of beauty of a group of women, we determine the median of the data.

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