NCERT Solutions for Exercise 14.4 Class 9 Maths Chapter 14

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

Edited By Sumit Saini | Updated on Jul 06, 2022 02:44 PM IST

NCERT solutions for exercise 14.4 Class 9 Maths chapter 14- In this section, we are going to be discussing new topics and concepts. . As from the previous exercise i.e. exercise 14.3, we know that statistics consist of many important topics like frequency, range, and different types of graphs in a single chapter of mathematics. Studying and analyzing other things to this exercise 14.4 Class 9 Maths is an extension exercise of exercise 14.2 of the chapter which had numerical problems based on frequency and range. In this exercise 14.4, we will be studying concepts mean, median and mode, in this right from formula to how it is going to be applied we will be studying all its methods sequentially.

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This Story also Contains

Statistics Class 9 Maths Chapter 14 Exercise: 14.4
More About NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4
Benefits of NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4
NCERT Solutions of Class 10 Subject Wise

The NCERT book Class 9 Maths chapter 14 exercise 14.4 also covers numerical exercise apart from theory it takes new terms into account like questions based on observations, maximum and minimum predicted values which are like the importance to it. This NCERT syllabus Chapter contains only real-life examples which are important and will be discussed in NCERT Solutions for Class 9 Maths chapter 14 exercise 14.4. Along with Class 9 Maths chapter 1 exercise 14.4 the following exercises are also present.

Statistics Class 9 Maths Chapter 14 Exercise: 14.4

Q1 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:

$Mean=\frac{Sum\ of\ observations}{Number \ of\ observations}$

Number of observations, n = 10

$\\\bar{X}=\frac{\sum_{i=1}^{n=10}x_{i}}{n}\\ \bar{X}=\frac{ 2+ 3+ 4+ 5+ 0+ 1+ 3+ 3+ 4+ 3}{10}\\ \bar{X}=\frac{28}{10}\\ \bar{X}=2.8$

Mean is 2.8

To find the median we have to arrange the given data in ascending order as follows:

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

n = 10 (even)

$\\Median=\frac{(\frac{n}{2})^{th}\ term+(\frac{n}{2}+1)^{th}\ term}{2}\\ Median=\frac{(\frac{10}{2})^{th}\ term+(\frac{10}{2}+1)^{th}\ term}{2}\\ Median=\frac{(5)^{th}\ term+(6)^{th}\ term}{2}\\ Median=\frac{3+3}{2}\\ Median=3$

In the given data 3 occurs the maximum number of times (4)

Therefore, Mode = 3

Q2 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:

$Mean=\frac{Sum\ of\ observations}{Number \ of\ observations}$

Number of observations, n = 15

$\\\bar{X}=\frac{\sum_{i=1}^{n=15}x_{i}}{n}\\ \bar{X}=\frac{41+ 39+ 48+ 52+ 46+ 62+ 54+ 40+ 96+ 52+ 98+ 40+ 42+ 52+ 60}{15}\\ \bar{X}=\frac{822}{15}\\ \bar{X}=54.8$

Mean is 54.8

To find the median we have to arrange the given data in ascending order as follows:

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

n = 15 (odd)

$\\Median=(\frac{n+1}{2})^{th}\ term\\ Median=(\frac{15+1}{2})^{th}\ term\\ Median=8^{th}\ term\\ Median=52$

In the given data 52 occurs the maximum number of times ()

Therefore, Mode = 52

Q3 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:

The given data is already in ascending order

Number of observations, n = 10 (even)

x + 1 = 63

x = 62

Q4 Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Answer:

In the given data 14 is occuring the maximum number of times (4)

Mode of the given data is therefore 14.

Q5 Find the mean salary of 60 workers of a factory from the following table:

Salary (in Rs)	Number of workers
3000	16
4000	12
5000	10
6000	8
7000	6
8000	4
9000	3
10000	1
Total	60

Answer:

Salary ( in Rs)(x _i )	Number of workers(f _i )	f _i x _i
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	$\sum_{i=1}^{8}f_{i}=60$	$\sum_{i=1}^{8}f_{i}x_{i}=305000$

The mean of the above data is given by

$\\\bar{X}=\frac{\sum_{i=1}^{8}f_{i}x_{i}}{\sum_{i=1}^{8}f_{i}}\\ \bar{X}=\frac{305000}{60}\\ \bar{X}=5083.33$

The mean salary of the workers working in the factory is Rs 5083.33

Q6 (i) Give one example of a situation in which the mean is an appropriate measure of central tendency.

Answer:

The mean is an appropriate measure of central tendency in case the observations are close to each other. An example of such a case is height of the students in a class.

Statistics Excercise: 14.4

Q6 (ii) Give one example of a situation in which the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Answer:

The mean is not an appropriate measure of central tendency in case the observations are not close to each other. An example of such a case is prices of the toys in a toy shop.

Benefits of NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4

The very first benefit in completing exercise 14.4 Class 9 Maths is right from all exercises covered in the chapter, it is also a favourite topic of an examiner to frame question form
Exercise 14.4 contains Questions related to the frequency and distributed data attached to Mean and median and questions related to grouping and ungrouping of data.
Students can have a better understanding in exercise 14.4 Class 9 Maths getting concepts over it will give an edge over others with best out of it as mentioned Class 9 Maths chapter 14 exercise 14.4
Class 9 Maths Chapter 14 exercise 14.4 is just a trailer for best problems to cover in future classes

Also, see-

NCERT Solutions of Class 10 Subject Wise

Frequently Asked Questions (FAQs)

1. Define Arithmetic Mean in statistics?

Ans: In mathematics and especially in statistics, the idea of mean is crucial. In a group of numbers, the mean is the average or most frequent value.

2. What do you mean by Median?

Ans: The median of a dataset listed in ascending order is a statistical metric that determines the middle value (i.e., from smallest to largest value)...

3. Can you explain Mode?

Ans: In data collection, the model is the value that appears the most frequently. A collection of data might have only one mode, several modes, or none at all.

4. What is the formula of Mean for discrete data?

Ans: .mean = fixi/xi where fi = frequency of discrete data and xi = discrete data

5. What is the difference between mean and median?

Ans: When a set of data is sorted in ascending or descending order, the mean is the average value, and the median is the midway value.

6. The number that appears the most frequently in a group of numbers is?

Ans: The number that appears the most frequently in a group of numbers is called MODE

7. The mode of 12, 17, 16, 15, 13, 11, 15 is?

Ans: The number 15 occurs the most(2 times) hence mode is 15 according to the definition.

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