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.

Conclusion

Class 7 Maths Chapter 3 Exercise 3.2 Solutions helps students learn how to find the mode and median in data sets. The mode is the number that appears most often, and the median is the middle number when data is in order. Practising Ex 3.2 Class 7 problems improves your ability to work with data. Focus on arranging the data correctly to find the median and spotting the most common number for the mode. These ideas are important for understanding basic data.

Class 7 Maths Chapter 3: Exercises Breakdown

CBSE Class 7 Maths Chapter 3 Other Study Materials

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