NCERT Solutions for Class 7 Maths Chapter 3: Data Handling - Exercise 3.2

1. The scores in mathematics test (out of 25) of students is as follows:

\[19,25,23,20,9,20,15,10,5,16,25,20,24,12,20\]

Find the mode and median of this data. Are they same?

Ans. Arranging data in ascending order

\[5,9,10,12,15,16,19,20,20,20,20,23,24,25,25\]

Mode is maximum occurring observation

Since \[20\] occurs \[4\] times,

Mode \[ = 20\]

Number of observation \[ = 15\]

Median \[ = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\]observation

\[ = {\left( {\dfrac{{15 + 1}}{2}} \right)^{th}}\]

\[ = {\left( {\dfrac{{16}}{2}} \right)^{th}}\]

\[ = {8^{{\text{th }}}}\]observation 

\[ = 20\]

So, both mode and median are \[20\]

Hence, they are same.

2. The runs scored in a cricket match by \[11\] players is as follows:

\[6,15,120,50,100,80,10,15,8,10,15\]

Find the mean, mode and median of this data. Are the three same?

Ans. Runs scored in the match $ = 6,15,120,50,100,80,10,15,8,10,15$

Arranging in ascending order $ = 6,8,10,10,15,15,15,50,80,100,120$,

Here, \[15\] occurs the maximum number of times. Hence, the mode of the data is \[15\]

Now,

Mean $ = \dfrac{{{\text{ Sum of scores }}}}{{{\text{ Number of players }}}}$

$ = \dfrac{{6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120}}{{11}}$

$ = \dfrac{{429}}{{11}} = 39$

Therefore, the mean score is \[39\]

Now, the median is the middle observation of the data.

There are \[11\] terms. 

Therefore, the middle observation is $\dfrac{{11 + 1}}{2} = {6^{th}}$ term

Therefore, the median of the data is \[15\] .

The mean, median and mode are not the same.

3. The weight (in ${\text{kg}}$) of \[15\] students of a class are:

\[38,42,35,37,45,50,32,43,43,40,36,38,43,38,47\]

(i) Find the mode and median of this data.

Ans. Given, weights of \[15\]students (in${\text{kg}}) = 38,42,35,37,45,50,32,43,43,40,36,38,43,38,47$

Arranging the data in ascending order $ = 32,35,36,37,38,38,38,40,42,43,43,43,45,47,50$

So, \[38\] and \[43\] both occur thrice. So, both \[38\] and \[43\] are the mode of the data.

Now, there are \[15\] values,

So, the median is the $\dfrac{{15 + 1}}{2} = {8^{th}}$ term

Hence, the median value is \[40\].

(ii) Is there more than one mode?

Yes, there are two modes in this data.

4. Find the mode and median of the data:

\[13,16,12,14,19,12,14,13,14\]

Ans. Given, \[13,16,12,14,19,12,14,13,14\]

Arranging in ascending order $ = 12,12,13,13,14,14,14,16,19$

Mode is that observation which occurs the maximum number of times.

Median is the middle observation of the data when the data is arranged in ascending or descending order.

So, \[14\]occurs thrice. 

So, the mode is \[14\].

Now, there are 9 values,

So, the median is the $\dfrac{{9 + 1}}{2} = {5^{{\text{th }}}}$ term

Hence, \[14\] is the median value.

5. Tell whether the statement is true or false:

(i) The mode is always one of the numbers in a data.

Ans. True.

Mode is that observation which occurs the maximum number of times.

(ii) The mean is one of the numbers in a data.

Ans. False.

(iii) The median is always one of the numbers in a data.

Ans. False.

For even number of observations, the median is the mean of the \[\dfrac{{n{\text{ }}}}{2}\] and \[{\left( {\dfrac{{n + 1}}{2}} \right)^{th}}\] values.

(iv) The data \[6,4,3,8,9,12,13,9\] has mean \[9.\]

Ans. Mean \[ = \dfrac{{{\text{ Sum of observations }}}}{{{\text{ Number of observations }}}}\]

\[ = \dfrac{{6 + 4 + 3 + 8 + 9 + 12 + 13 + 9}}{8}\]

\[ = \dfrac{{64}}{8}\]

\[ = 8\]

Hence, the statement is False.

Class 7 Maths Chapter 3 Exercise 3.2 Solutions

Class 7 Maths Chapter 3 exercise 3.2 comprises of all the basic fundamentals of data handling. Effective learning of exercise 3.2 class 7 will help you build a strong foundation in data handling. It deals with significant concepts such as Mean, Mode, Median, and Mode of Large Data. Other important topics covered in this chapter include Collection of Data, Organization of Data, Arithmetic Mean, Usage of Bar Graphs with Different Purposes, Double Bar Graph Construction and Scale Choosing. This chapter also covers topics related to chance and probability.

NCERT Solutions for Class 7 Maths Chapter 3 Exercise 3.2 have been created to facilitate complete conceptual clarity. They comprise all required solved examples, formulas, practice exercises, and question answers. They contain all possible and probable question types to ensure that you are not only familiar with all kinds of questions that can be asked in your exam but also help you become very thorough with the subject. Some of the question types covered includes multiple-choice questions, true or false questions, find the mean, median mode kind of questions etc. All solutions follow a step by step format to minimize confusion and maximize clarity.

NCERT Maths Class 7 Chapter 3 Exercise 3.2 solutions are exhaustive, comprehensive and to the point. They are a hundred per cent accurate, easy to understand and remember. With Vedantu as your learning partner, you can learn anywhere and anytime. NCERT Solutions Class 7 Maths Chapter 3 Exercise 3.2 are very effort and time-saving solutions that are based on established study strategies. They make both learning and revision sessions effective. They contain an ample number of practical problem sums that enhance your practice and help you gain more confidence in the subject. Vedantu’s NCERT Solutions contain the simplest, most logical and shortest solutions to all problems pertaining to Data Handling Class 7 Exercise 3.2.

For scoring high marks in exams, it is as important to be thorough with the subject as it is to develop other relevant skills such as quick technique application, fast problem sum type identification, accurate problem solving, and speedy problem sum solving. NCERT Class 7 Maths Chapter 3 Exercise 3.2 PDF will help you develop all the requisite skills to pass your examination with flying colours.

Vedantu’s highly qualified subject experts make maximum efforts to prepare NCERT Solutions that ensure that learning the Class 7 Maths syllabus is interesting, engaging, fun, and interactive. 

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