Exercise 3.4 (Revised) - Chapter 3 - Data Handling - Ncert Solutions class 7 - Maths

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Chapter 3: Data Handling - NCERT Solutions for Class 7 Maths | Comprehensive Guide

Example 1

Ashish studies for 4 hours, 5 hours and 3 hours respectively on three consecutive days. How many hours does he study daily on an average?

Solution

The average study time of Ashish would be
$
\frac{\text { Total number of study hours }}{\text { Number of days for which he studied }}=\frac{4+5+3}{3} \text { hours }=4 \text { hours per day }
$

Thus, we can say that Ashish studies for 4 hours daily on an average.
Example 2

A batsman scored the following number of runs in six innings:
$
36,35,50,46,60,55
$

Calculate the mean runs scored by him in an inning.
Solution

Total runs $=36+35+50+46+60+55=282$.
To find the mean, we find the sum of all the observations and divide it by the number of observations.
Therefore, in this case, mean $=\frac{282}{6}=47$. Thus, the mean runs scored in an inning are 47 .

Example 3

The ages in years of 10 teachers of a school are:
$
32,41,28,54,35,26,23,33,38,40
$
(i) What is the age of the oldest teacher and that of the youngest teacher?
(ii) What is the range of the ages of the teachers?
(iii) What is the mean age of these teachers?

Solution
(i) Arranging the ages in ascending order, we get:
$
23,26,28,32,33,35,38,40,41,54
$

We find that the age of the oldest teacher is 54 years and the age of the youngest teacher is 23 years.

Example 4

Find the mode of the given set of numbers: 1, 1, 2, 4, 3, 2, 1, 2, 2, 4
Solution

Arranging the numbers with same values together, we get
$
1,1,1,2,2,2,2,3,4,4
$

Mode of this data is 2 because it occurs more frequently than other observations.

Example 5

Following are the margins of victory in the football matches of a league.
$
\begin{aligned}
& 1,3,2,5,1,4,6,2,5,2,2,2,4,1,2,3,1,1,2,3,2, \\
& 6,4,3,2,1,1,4,2,1,5,3,3,2,3,2,4,2,1,2
\end{aligned}
$

Find the mode of this data.
Solution

Let us put the data in a tabular form:

Looking at the table, we can quickly say that 2 is the 'mode' since 2 has occured the highest number of times. Thus, most of the matches have been won with a victory margin of 2 goals.

Example 6

Find the mode of the numbers: $2,2,2,3,3,4,5,5,5,6,6,8$
Solution

Here, 2 and 5 both occur three times. Therefore, they both are modes of the data.

Example 7

Find the median of the data: $24,36,46,17,18,25,35$
Solution

We arrange the data in ascending order, we get $17,18,24,25,35,36,46$ Median is the middle observation. Therefore 25 is the median.

Example 8

 Two hundred students of $6^{\text {th }}$ and $7^{\text {th }}$ classes were asked to name their favourite colour so as to decide upon what should be the colour of their school building. The results are shown in the following table. Represent the given data on a bar graph.

Answer the following questions with the help of the bar graph:
(i) Which is the most preferred colour and which is the least preferred?
(ii) How many colours are there in all? What are they?

Solution

Choose a suitable scale as follows:
Start the scale at 0 . The greatest value in the data is 55 , so end the scale at a value greater than 55 , such as 60 . Use equal divisions along the axes, such as increments of 10 . You

know that all the bars would lie between 0 and 60 . We choose the scale such that the length between 0 and 60 is neither too long nor too small. Here we take 1 unit for 10 students.
We then draw and label the graph as shown.
From the bar graph we conclude that
(i) Blue is the most preferred colour (Because the bar representing Blue is the tallest).
(ii) Green is the least preferred colour. (Because the bar representing Green is the shortest).

(iii) There are five colours. They are Red, Green, Blue, Yellow and Orange. (These are observed on the horizontal line)

Example 9

 Following data gives total marks (out of 600 ) obtained by six children of a particular class. Represent the data on a bar graph.

Solution
(i) To choose an appropriate scale we make equal divisions taking increments of 100 . Thus 1 unit will represent 100 marks. (What would be the difficulty if we choose one unit to represent 10 marks?)
(ii) Now represent the data on the bar graph.

Example 10

 A mathematics teacher wants to see, whether the new technique of teaching she applied after quarterly test was effective or not. She takes the scores of the 5 weakest children in the quarterly test (out of 25 ) and in the half yearly test (out of 25):

Solution

She draws the adjoining double bar graph and finds a marked improvement in most of the students, the teacher decides that she should continue to use the new technique of teaching.