Jasmine Grover Content Strategy Manager
Content Strategy Manager
In this chapter, we will focus on bar charts as a method for displaying data.
Bar diagrams (or bar charts) are one of the earliest and most widely utilised data presentation diagrams. Each bar in a bar chart is a broad rectangle. The height of the bar determines the value of the bar's reading.
Bar diagrams are visual aides for presenting statistical data. Frequently, different colours, tints, spots, dashes, etc. are applied to the bars in bar charts to differentiate between the continuous variables being represented. There will always be an index explaining the meanings of the various colours, tones, and markings.
Each bar diagram has a title (displayed either at the top or bottom of the diagram) that describes the subject depicted in the diagram. In addition, there may be footnotes at the bottom of the diagram to elucidate information not included in the title. The student is advised to read these footnotes with extreme caution and to not disregard these facts when interpreting bar diagrams.
One axis (typically the x-axis) of each bar diagram represents a discrete variable, while the other axis represents the scale for one or more continuous variables.
Topics to be covered in this section:-
- Types of Bar charts
- CAT Previous year questions on Bar Charts.
- How to approach CAT questions on Bar charts
Types of Bar charts
Simple bar chart
One continuous variable and one discrete variable are plotted on the simple bar chart, the 'simplest' type of bar chart.
Simple bar chart
Stacked bar chart
On a bar chart, the length of a bar typically represents the magnitude of a singular continuous variable. In certain instances, however, it may be possible and even necessary to decompose the magnitude of the primary continuous variable into its component portions. When this type of representation is employed, the resulting chart is known as a layered bar chart.
Stacked bar chart
Various hues, colours, etc. are employed to differentiate the various components, and an index is provided alongside the chart to elucidate these distinctions.
Composite Bar chart
The inability to depict more than one continuous variable is one of the primary limitations of the plain bar chart. Similarly, a stacked/component bar chart can only display multiple continuous variables if their sum equals a single continuous variable. In other terms, only one continuous variable and its components can be displayed.
Composite Bar chart
However, if two or more sets of continuous variables are to be displayed on the same bar chart, a composite bar chart is utilised.
Deviation bar
Deviation bars are valuable for the graphical presentation of continuous variables with both positive and negative values, such as surplus or deficit, net profit or loss, and net imports and exports. In general, bar charts best represent continuous variables with both positive and negative values.
Deviation bar
Positive deviations (loss or deficit) are represented by bars below the base line, whereas positive deviations (profit or surplus) are represented by bars above the base line.
CAT Previous year questions on Bar Charts.
(Q. Nos. 1-2) Refer to the charts below and answer the questions that follow.
Chart given below presents the sources of local and state tax revenues for the year 2001 as a percentage of the total tax revenues. (CAT 2015)
The diagram shown below represents the combined state and local tax revenue (in $ mn).
Ques 1. Find the difference between the tax revenue generated from individual income at local and state levels in 2001. $ _______ mn.
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Solution:-
State tax revenue from individual income = 17 × 525/100 = $ 89.25 mn
Local tax revenue from individual income = 2 × 525/100 = $ 10.5 mn
Difference = 89.25 − 10.5 = $78.75 mn
Ques 2. If revenue distribution in 2000 was same as in 2001 and tax from highway users was collected for the first time, then what was the percentage increase in tax revenue from source other than highway users in 2000 over the previous year? _______ %.
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Solution:-
Tax revenue from highway users in 2000 = 8 × 500/100 = $40.0 mn
Tax revenue from other sources in 2000 = 500 − 40 = $ 460 mn
Percentage increase in tax revenue from other sources = (460 – 440)/440 × 100 = 4.5%
Directions (Q. Nos. 3-7) Study the graph carefully and answer the following questions. (CAT 2009)
Ques 3. In which year the value per packet was minimum?
(a) 2005 (b) 2006 (c) 2007 (d) 2008
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Solution:- (a)
In 2005 = (150/1.0)= Rs.150
In 2006 =(330/0.75)= Rs.200
In 2007 =(330/1.5)= Rs.220
In 2008 =(400/1.6)= Rs.250
In 2009 =(500/2.0)= Rs.250
Ques 4. What was the difference between the packets exported in 2007 and 2008?
(a) 10 (b) 1000 (c) 100000 (d) 1000000
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Solution:- (d)
Difference
between the packets exported in 2007 and 2008 is = 160 lakh − 150 lakhs = 10 lakh
Ques 5. What was the approximate per cent increase in export value from 2005-2009?
(a) 350 (b) 330 (c) 43 (d) None of these
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Solution:-
Percentage increase in export value from 2005 – 2009
= \(\frac{500-150}{150}\) × 100 = \(\frac{350}{150}\) × 100% = 233.33%
Ques 6. What was the percentage drop in export quantity from 2005-2006?
(a) 75 (b) 25 (c) 50 (d) None of these
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Solution:- (b)
Percentage decrease in export value from 2005 – 2006
=\(\frac{100-75}{100}\) × 100 = \(\frac{25}{100}\) × 100% = 25%
Ques 7. If in the year 2008, the packets were exported at the same rate per packet as that in 2007, what was value in crores of rupees of export in 2008?
(a) 400 (b) 352 (c) 375 (d) 360
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Solution:- (b)
Cost of one packet = (330 cr) = Rs. 220
In 2008, the export value
= 160 lakh × 220
= (1.60 × 220) cr = Rs 352 cr
Directions (Q. Nos. 8-12) Study the graph carefully and answer the following questions. (CAT 2009)
Ques 8. In which year did the import register highest increase over its preceding year?
(a) 2004 (b) 2005 (c) 2006 (d) 2009
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Solution:- (c)
Increase in import in
2004 over 2003 = 2413 − 1811 = 602
2005 over 2004 = 4203 − 2413 = 1790
2006 over 2005 = 7016 − 4203 = 2813
2009 over 2008 = 2500 − 2000 = 500
Increase in import was highest in 2006.
Ques 9. The import in 2007 was approximately how many times that of the year 2003?
(a) 0.31 (b) 1.68 (c) 2.41 (d) 3.22
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Solution:- (d)
Let in 2007 the imports be X times to that of 2003
X × 1811=5832
X=3.22
Ques 10. What is the ratio of the years which have above average import to those which have below average imports?
(a) 5 : 3 (b) 8 : 3 (c) 3 : 8 (d) None of these
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Solution:- (d)
Average Imports = \(\frac{3465+1811+2413+4203+7016+5832+2000+2500}{8}\)=3655
No of year when imports are above average = 3 (2005,2006 and 2007)
No of year when imports are below average = 5 (Rest all)
Required ratio = 3:5
Ques 11. The increase in imports in 2009 was what per cent of the import in 2008?
(a) 25 (b) 5 (c) 125 (d) 80
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Solution:- (a)
Increase in year 2009 as compared to year 2008 = 2500 − 2000 = 500
Hence, required percentage = 500/2000 × 100 = 25%
Ques 12. The import in 2005 is approximately what per cent of the average import for the given years? (a) 125 (b) 115 (c) 190 (d) 85
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Solution:- (b)
Average import for the given years: 3655
Import in the year 2005 = 4203
∴ x% of 3655=4203
X= (4203 x 100)/ 3655 = 115%
Directions (Q. Nos. 13-16) Answer the following questions based on the information given below. (CAT 2008)
The bar chart below shows the revenue received, in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.
Ques 13. The difference between the estimated subscription in Europe in 2008 and what it would have been if it were computed using the percentage growth rate of 2007 (over 2006), is closest to
(a) 50 (b) 80 (c) 20 (d) 10(e) 0
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Solution:- (a)
Subscription in Europe in 2006 = 380 USD Subscription in Europe in 2007 = 500 USD
Per cent growth rate in 2007 over 2006 = (500 – 380)/380 × 100 = 31.5% ≈ 30%
the subscription in 2008 should have been = 500 × 1.3 = 650 USD (approx.)
So, difference from the estimated subscription = (650 − 600) = 50 USD
Ques 14. In 2003, sixty per cent of subscribers in Europe were men. Given that women subscribers increase at the rate of 10% per annum and men at the rate of 5% per annum, what is the approximate percentage growth of subscribers between 2003 and 2010 in Europe? The subscription prices are volatile and may change each year.
(a) 62 (b) 15 (c) 78 (d) 84(e) 50
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Solution:- (a)
Let the number of subscribers be 100x.
Number of Men = 60x
Number of men in 2010 = 60x × (1.03)7 = 84.42x (approx.) Number of women = 40x
Number of women in 2010 = 40x × (1.1)7 = 77.94x (approx.)
Therefore, the total number of subscribers = 84.42x + 77.94 = 162.36x
∴Percentage growth of subscribers = (162.36x − 100x)/(100x) = 62.36 (approx.)
Ques 15. Consider the annual per cent change in the gap between subscription revenues in the US and Europe. What is the year in which, the absolute value of this change is the highest?
(a) 03-04 (b) 05-06 (c) 06-07 (d) 08-09 (e) 09-10
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Solution:- (d)
Gap in 2008 = 780 − 600 = 180 USD Gap in 2009 = 810 − 700 = 110 USD
∴ Annual percentage change = ((110 – 180)/180) × 100 = − 39%
Absolute change = 39%
∴In year 2008-09 the value of absolute change is highest.
Ques 16. While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the per cent change in growth rate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)?
(a) 17 (b) 20 (c) 35 (d) 60 (e) 100
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Solution:- (c)
Growth rate of 2007 =(500 – 380)/380 × 100 = 31.58%
Growth rate of 2005 = (280 – 190)/190 × 100 = 47.37%
Per cent change in growth rate of 2007 in relation to growth rate of 2005
=(47.37 − 31.58)/47.37 × 100 ≈ 35%
How to approach Bar charts questions on CAT
- Student should have a basic understanding of reading bar graphs/charts
- Basic addition, subtraction, division and multiplication related to numbers on bar graphs
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