Use of Bar Graphs with a Different Purpose
We have seen last year how information collected could be first arranged in a frequency distribution table and then this information could be put as a visual representation in the form of pictographs or bar graphs. You can look at the bar graphs and make deductions about the data. You can also get information based on these bar graphs. For example, you can say that the mode is the longest bar if the bar represents the frequency.
Choosing a Scale
We know that a bar graph is a representation of numbers using bars of uniform width and the lengths of the bars depend upon the frequency and the scale you have chosen.
For example: In a bar graph where numbers in units are to be shown, the graph represents one unit length for one observation and if it has to show numbers in tens or hundreds, one unit length can represent 10 or 100 observations. Consider the following examples:
Two hundred students of 6th and 7th 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.
| Favourite Colour | Number of Students |
|---|---|
| Red | 43 |
| Green | 19 |
| Blue | 55 |
| Yellow | 49 |
| Orange | 34 |
Solution :
Lets first 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
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 5 students.
One the X-axis we represent each color with a scale of 10.
We then draw and label the graph as shown. The first bar is drawn for you, draw the bar graphs for remaining colours.
We see that green is 19. So start from the green point at 10 on x-axis and drag and draw a rectangle bar upto height 19.
Great. Now do the same for Blue.
Red, Green and Blue done. Now do the same for Yellow.
Just one more left. Draw the bar for Orange.
All done. We have drawn a bar graph representation of the tabular data provided. Now answer the following questions with the help of the bar graph:
(i) Which is the most preferred colour and which is the least preferred?
Solution :
(ii) How many colours are there in all? What are they?
Solution : There are
Following data gives total marks (out of 600) obtained by six children of a particular class. Represent the data on a bar graph.
| Students | Marks Obtained |
|---|---|
| Ajay | 450 |
| Bahubali | 500 |
| Deepak | 300 |
| Farzi | 360 |
| Sushma | 400 |
| Devi | 540 |
Drawing double bar graph
Consider the following two collections of data giving the average daily hours of sunshine in two cities Delhi and Mumbai for all the twelve months of the year.
In Delhi
| Average hours ofsunshine | Jan | Feb | Mar | Apr | May | June | July | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 5.5 | 6 | 6 | 7 | 8 | 7 | 6 | 6 | 6 | 5 | 4 |
In Mumbai
| Average hours ofsunshine | Jan | Feb | Mar | Apr | May | June | July | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4.5 | 4.5 | 6 | 8 | 8 | 7 | 7 | 7 | 6 | 5 | 4 |
By drawing individual bar graphs you could answer questions like
(i) In which month does each city has maximum sunlight? or
(ii) In which months does each city has minimum sunlight?
However, to answer questions like “In a particular month, which city has more sunshine hours”, we need to compare the average hours of sunshine of both the cities.
To do this we will learn to draw what is called a double bar graph giving the information of both cities side-by-side. This bar graph shows the average sunshine of both the cities.
For each month we have two bars, the heights of which give the average hours of sunshine in each city. From this we can infer that except for the month of April, there is always more sunshine in Mumbai than in Delhi. You could put together a similiar bar graph for your area or for your city.
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).
| Students | Quarterly | Half yearly |
|---|---|---|
| Ashish | 10 | 15 |
| Arun | 15 | 18 |
| Devesh | 12 | 16 |
| Priya | 20 | 21 |
| Suma | 9 | 15 |
Solution :
She draws the adjoining double bar graph. Look at the graph can you quickly say whether the marks have improved?
1. The bar graph shows the result of a survey to test water resistant watches made by different companies.
Each of these companies claimed that their watches were water resistant. After a test the above results were revealed.
(a) Can you work out a fraction of the number of watches that leaked to the number tested for each company?
Solution:
A fraction of the number of watches that leaked to the number tested for each company are :
For A,
For B,
For C,
For D,
(b) Could you tell on this basis which company has better watches?
Clearly , 10<15<20<25
=
Thus, a company with a fraction
2.Sale of English and Hindi books in the years 1995, 1996,1997 and 1998 are given below:
| Years | 1995 | 1996 | 1997 | 1998 |
|---|---|---|---|---|
| English | 350 | 400 | 450 | 620 |
| Hindi | 500 | 525 | 600 | 650 |
Draw a double bar graph and answer the following questions:
(a) In which year was the difference in the sale of the two language books least?
To choose an appropriate scale, we make equal divisions taking increments of 100. Thus, 1 unit = 100 books.
Clearly, the difference in the sale of the two language books is least in the year
(b) Can you say that the demand for English books rose faster? Justify.
Since, the bar graph of the sale, of English books becomes longer faster, so the demand for English books rose