NCERT Solutions for Class 9 Maths Chapter 14: Statistics - Exercise 14.4

Exercise 14.4

1. The following number of goals was scored by a team in a series of \[10\] matches:

\[\text{2, 3, 4, 5, 0, 1, 3, 3, 4, 3}\]

Find the mean, median and mode of these scores.

Ans: It is given that the number of goals scored by the team is

\[\text{2, 3, 4, 5, 0, 1, 3, 3, 4, 3}\].

The formula for calculating the Mean of any data is given by:

\[\text{Mean of data=}\frac{\text{Sum of all observations}}{\text{Total number of observations}}\]

Therefore, \[\text{Mean score=}\frac{\text{2+3+4+5+0+1+3+3+4+3}}{\text{10}}\]

\[\text{=}\frac{\text{28}}{\text{10}}=2.8\]

\[2.8goals\]

Now arranging the number of goals in ascending order to calculate the median of the given data,

\[\text{0, 1, 2, 3, 3, 3, 3, 4, 4, 5}\]

Since the number of observations is an even number, that is, \[\text{10}\]. Hence, the mean of \[\frac{10}{2}\] i.e., \[{{5}^{th}}\]  and \[\frac{\text{10}}{\text{2}}\text{+1}\] i.e., \[{{6}^{th}}\] observation, while arranged in ascending or descending, will give us the median.

Therefore, \[\text{Median score=}\frac{{{\text{5}}^{\text{th}}}\text{observation+}{{\text{6}}^{\text{th}}}\text{observation}}{\text{2}}\]

\[\text{=}\frac{\text{3+3}}{\text{2}}=3\].

The observation with maximum frequency is the Mode of the data. 

Since the frequency of \[3\] is maximum, therefore the mode score of data is \[3\].

2. In a mathematics test given to \[\text{15}\] students, the following marks (out of \[\text{100}\]) are recorded: 

\[\text{41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60}\]

Find the mean, median and mode of this data. 

Ans:

The formula for calculating the Mean of any data is given by:

\[\text{Mean of data=}\frac{\text{Sum of all observations}}{\text{Total number of observations}}\]

\[\text{=}\frac{\text{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}}{15}\]

\[\text{=}\frac{\text{822}}{\text{15}}\text{=54}\text{.8}\].

Now arranging the scores obtained by \[\text{15}\] students in an ascending order, 

\[\text{39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98}\]

Since the number of observations is an odd number, that is, \[\text{15}\]. Hence, the median of data will be \[\frac{\text{15+1}}{\text{2}}\text{=}{{\text{8}}^{\text{th}}}\text{observation}\], while arranged in ascending or descending. 

Therefore, median score of data \[\text{=52}\]. 

The observation with maximum frequency is the Mode of the data.

Since the frequency of \[\text{52}\] is maximum, therefore the mode score of the data is \[\text{52}\].

3. The following observations have been arranged in ascending order. If the median of the data is \[\text{63}\], find the value of \[\text{x}\]. 

\[\text{29, 32, 48, 50, x, x + 2, 72, 78, 84, 95}\]

Ans: Since the number of observations is an even number, that is, \[\text{10}\]. Hence, the mean of \[\frac{10}{2}\] i.e., \[{{5}^{th}}\]  and \[\frac{\text{10}}{\text{2}}\text{+1}\] i.e., \[{{6}^{th}}\] observation, while arranged in ascending or descending, will give us the median.

Therefore, \[\text{Median of }data\text{=}\frac{{{\text{5}}^{\text{th}}}\text{observation+}{{\text{6}}^{\text{th}}}\text{observation}}{\text{2}}\]

\[\Rightarrow \text{63=}\frac{\text{x+x+2}}{\text{2}}\]

\[\Rightarrow \text{63=}\frac{\text{2x+2}}{\text{2}}\]

\[\Rightarrow \text{63=x+1}\]

\[\Rightarrow \text{x=62}\]

4. Find the mode of \[\text{14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18}\].

Ans:

Firstly, arranging the data in an ascending order,

\[\text{14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28}\]

The observation with maximum frequency is the Mode of the data.

Since the frequency of \[\text{14}\] is maximum, therefore the mode of the given data is \[\text{14}\].

5. Find the mean salary of \[\text{60}\] workers of a factory from the following table:

Ans. The formula for  calculating the mean is give by:

\[Mean=\frac{\sum{{{f}_{\text{i}}}{{\text{x}}_{\text{i}}}}}{\sum{{{f}_{\text{i}}}}}\]

The value of \[\sum{{{f}_{\text{i}}}{{\text{x}}_{\text{i}}}}\] and \[\sum{{{f}_{\text{i}}}}\] can be calculated as follows:

So, Mean salary \[\text{=}\frac{\text{305000}}{60}\].

Therefore, the mean salary of \[\text{60}\] workers is \[\text{Rs}\text{. 5083}\text{.33}\].

6. Give one example of a situation in which 

i. The mean is an appropriate measure of central tendency. 

Ans: Mean is an appropriate measure of central tendency when the observations are relatively close to each other.

Median is an appropriate measure of central tendency when the observations are relatively far from each other.

Consider the following example − the following data represents the heights of the members of a family:

\[\text{154}\text{.9 cm, 162}\text{.8 cm, 170}\text{.6 cm, 158}\text{.8 cm, 163}\text{.3 cm, 166}\text{.8 cm, 160}\text{.2 cm}\]

In this case, mean will be calculated as an appropriate measure of central tendency because the observations in the given data are close to each other.

ii. The mean is not an appropriate measure of central tendency, but the median is an appropriate measure of central tendency.

Ans: Mean is an appropriate measure of central tendency when the observations are relatively close to each other.

Median is an appropriate measure of central tendency when the observations are relatively far from each other.

Consider the following data representing the marks obtained by \[\text{12}\] students in a test. 

\[\text{48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99}\]

In this case, the median will be calculated as an appropriate measure of central tendency because there are some observations which are very far from other observations.

NCERT Solutions for Class 9 Maths

• Chapter 1 - Number System

• Chapter 2 - Polynomials 

• Chapter 3 - Coordinate Geometry

• Chapter 4 - Linear Equations in Two Variables

• Chapter 5 - Introductions to Euclid's Geometry

• Chapter 6 - Lines and Angles

• Chapter 7 - Triangles

• Chapter 8 - Quadrilaterals

• Chapter 9 - Areas of Parallelogram and Triangles

• Chapter 10 - Circles

• Chapter 11 - Constructions

• Chapter 12 - Heron's formula

• Chapter 13 - Surface area and Volumes

• Chapter 14 - Statistics

• Chapter 15 - Probability

NCERT Solution Class 9 Maths of Chapter 14 All Exercises

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.4

Opting for the NCERT solutions for Ex 14.4 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 14.4 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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