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NCERT · Class 9 · Maths

Chapter 12: Statistics

Practice each question, then open the answer or worked solution.

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Exercise 14.4

Textbook page 269 · 6 questions
Q1Written answer

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.

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Worked solution

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

Here,

Number of observations (n) = 10

Since the number of observations is even, the median can be calculated as

Ncert solutions class 9 chapter 14-15

= 3

Mode

To find the mode, we first arrange the data in ascending order.

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Here,

We find that 3 occurs most frequently (4 times).

∴ Mode = 3

Q2Written answer

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.

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Worked solution

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

Here,

Number of observations (n) = 15

Since the number of observations is odd, the median can be calculated as

Median = [(n+1)/2]th observation

= [(15+1)/2]th observation

= (16/2)th observation

= 8th observation

= 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

Q3Written answer

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

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Worked solution

Number of observations (n) = 10

Given that Median = 63

Since the number of observations is even, the median can be calculated as

Ncert solutions class 9 chapter 14-16

63 = [5th observation+(5+1)th observation]/2

63 = [5th observation+6th observation]/2

63 = (x+x+2)/2

63 = (2x+2)/2

x = 63-1

x = 62

Q4Written answer

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

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Worked solution

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

Q5Written answer

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

Ncert solutions class 9 chapter 14-17

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Worked solution
Salary (xi) 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 Σfi = 60 Σfixi = 305000

Ncert solutions class 9 chapter 14-18

The mean salary is ₹5083.33

Q6Written answer

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.

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Worked solution

(i) Mean marks obtained in the examination

(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

= 4th observation

= 56