NCERT Solutions Class 9 Maths Chapter 14 Statistics Ex 14.4

NCERT Solutions Class 9 Maths 
Chapter – 14 (Statistics) 

The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 14 Statistics Exercise 14.4 has been provided here to help the students in solving the questions from this exercise. 

Chapter 14: Statistics

• NCERT Solution Class 9 Maths Ex – 14.1
• NCERT Solution Class 9 Maths Ex – 14.2
• NCERT Solution Class 9 Maths Ex – 14.3

Exercise – 14.4

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 – 
Mean = Average = Sum of all the observations/Total number of observations
= (2+3+4+5+0+1+3+3+4+3)/10
= 28/10
= 2.8

Median
To find the median, we first arrange the data in ascending order.
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
The number of observations is 10, which is an even number. Therefore, the median score will be the average of 10/2 i.e., 5th and 10/2 + 1 i.e., 6th observation while arranged in ascending or descending order.
Median score = (5^th observation + 6^th observation)/2
= (3 + 3)/2
= 6/2
= 3

Mode
To find the mode, we first arrange the data in ascending order.
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
We find that 3 occurs most frequently (4 times)
∴ Mode = 3

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 –
Mean = Average = Sum of all the observations/Total number of observations
= (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60)/15
= 822/15
= 54.8

Median
To find the median, we first arrange the data in ascending order.
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
As the number of observations is 15 which is odd, therefore, the median of data will be (15 + 1)/2 = 8^th observation
Therefore, the median of the data = 52

Mode
To find the mode, we first arrange the data in ascending order.
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
Here,
We find that 52 occurs most frequently (3 times)
∴ Mode = 52

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 –
Since the number of observations is even, the median can be calculated as
Therefore, the median of this data will be the average of 10/2 i.e., 5^th and 10/2 + 1 i.e., 6^th observation.
Therefore, median of the data = (5^th observation + 6^th observation) / 2
⇒ 63 = (x + x + 2) / 2
⇒ 63 = (2x + 2) / 2
⇒ 63 = x + 1
∴ x = 62

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

Answer –
Mode
To find the mode, we first arrange the given data in ascending order.
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here,
We find that 14 occurs most frequently (4 times)
∴ Mode = 14

5. Find the mean salary of 60 workers in a factory from the following table.

Answer – 

The grouped mean for data with different proportions is given by the formula ∑f_ix_i / ∑f_i
The value of ∑f_ix_i and ∑f_i can be calculated as follows:

Mean salary = 305000/60 = 5083.33
Therefore, the mean salary of 60 workers is ₹ 5083.33.

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) Consider the following example − The following data represent the heights of the members of a family:
154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm
In this case, it can be observed that the observations in the given data are close to each other.
Therefore, the mean will be an appropriate measure of central tendency.

(ii) Runs scored by Mahendra Singh Dhoni in 7 matches are
39, 51, 56, 102, 83, 48, 91
Here,
Mean = (39 + 51 + 56 + 102 + 83 + 48 + 91)/7
= 470/7
= 67.1.

Median
Arranging in ascending order, we get 39, 48, 51, 56, 83, 91, 102
n = 7
Median = [(n+1)/2]^th observation
= ( (7+1)/2)^th observation
= (8/2)^th observation
= 4^th observation
= 56