Quantitative Techniques Question Pattern of Bar Graphs Explained for CLAT 2020

Read carefully to understand Quantitative Techniques Question Pattern

Bar Graph

A​​ bar graph/charts​​ are visually represented data in the form of Bars (thick box) which is usually used for comparing information. These charts can be formed with horizontal bars or vertical bars.​​ The value of reading of the bar is determined by the height of the bar.​​ 

Some keynotes to solve any type of bar graph:

  • As bar graphs are visual aids, an explanatory index is always given in the question which is indicating the meanings of different colours and markings. Make sure to read it thoroughly and cross-check it before marking an answer.

  • A bar graph would always have a title (indicating subject matter) or footnote explaining facts that aren’t covered in the title. Read it carefully and make a mental note of it as it may consist of units that u may mistake while solving the question.

  • One axis (usually x-axis) will represent a discrete variable(independent variable)​​ while the other axis is the representation of the scale of one or more continuous variables. Observe the pattern of height and make deductions accordingly.

Types of Bar Graphs:

  • Simple bar graph: Horizontal graph

Discrete​​ information is mentioned in y-axis while continuous information is mentioned in the x-axis. The bars are aligned horizontally in this type of bar graph.

 

Sample Problem:​​ The following bar chart shows the data for sales of computer in various years. Study the graph to answer the questions.

 

Observation-based on the graph: From 2010 to 2014, no. of computers sold has been continuously declining. The only increase in sales has been observed from 2014-2015.​​ 

 

  • Find the percentage increase in the number of computers sold from 2014 to 2015.

  • 55%  (b) 45%​​   (c) 68%  (d) 88%

Solution:​​ In 2015, no. of computers sold is 32000 while the no. of computers sold in 2014 is 19000. Thus increase in the no. of units​​ of computers sold is 32000-19000= 13000 units. As the base year would be 2014 because the comparison has to be done with 2014 only. Therefore percentage change would be 13000*100/19000= 68.4%. As in the question, the numbers are absolute, we would mark (c) option.

  • Which two years sales of computers when combined would approximately give sales figure of 2010.

(a)2011 & 2012  (b) 2013 & 2014

(c)2012 & 2013​​   (d) 2014 & 2015

Solution:​​ Always try to solve such question orally by looking directly at options. As in quant a lot of time can be saved by using options. Sale of 45000 computers in 2010 if divided into almost two parts can be considered as 22000 and 23000. The only years with close to these numbers are 2013 and 2014. Thus answer (b) would be the answer. Here the sum of the sales figure is not giving exact 45000 and question says approximately thus the closest option would be marked.

Also, if you check other options like (a) then you will find out that in 2011, 2012 and 2015 the sales figure is more than 30000. If you add the lowest sales figure(19000) to 30000 it will be 49000 which is beyond 45000. Thus all other options can be eliminated with that logic.

  • Between two years the rate of change in sales of computers is minimum:

  • 2010-2011(b) 2011-2012  (c) 2012-2013  (d)2013-2014

Solution:​​ For this question, you will have to check the percentage change in all successive years. In 2010-2011, the percentage change is 11%, In 2011-2012, the percentage change is 10%, In 2012-2013, the percentage change is 31% while In 2013-2014, the percentage change is 24%. Thus the lowest rate of change is​​ 10%. The answer will be option(b).

  • Simple Bar Graph: Vertical Graph

Discrete information like year, country etc., in the x-axis, while information that is continuous is mentioned in the y-axis. The bars are aligned vertically in such graphs.​​ 

The problem for Vertical graph and horizontal graph are not different, the only difference in both is the alignment of bars.

  • Stacked Graph

When a single continuous variable magnitude needs to be broken into different small components it is known as a stacked bar chart or Component bar chart.

These bars are sequentially stacked one above the other in a single graph (either vertically or horizontally). The length of the bar with a single colour or pattern gives information about a single commodity or any variable. And information about other variable/commodity is above/beside that with different pattern or colour. The graph can even have more than 2 variables stacked one above the other. The break up of bars within a bar is usually done on percentage bais although you might find unitary division in the bars and then also the complete length will give the total no. of units and break up will be considered as a part of that total.​​ 

Sample Problem:​​ Below given graph represents the number of units sold of products A, B, C and D over 5 year period.​​ Study the following graph carefully and answer the questions accordingly.

  

  • What is the percentage​​ change in the total no. of​​ products sold​​ from 2002 to 2003?

(a)35%  (b) 128%(c)​​ 22%(d) 28%

Solution:​​ In this particular question percentage change is the keyword for the solution, as it is not mentioned increase or decrease from 2002 to 2003 one might get confused in taking the base for calculating the percentage change.

As asked about the percentage change in total units of 2002 and 2003, first add no. of A, B, C, D products in both the year i.e., for 2002: 930+245+225+445 = 1800 & 2003: 370+350+355+725=2300. For percentage change, the difference in both the year numbers will be in the numerator i.e., 2300-1800 = 500, and as the change has been asked wrt 2002 the base/denominator will be 2300.

Percentage change = 500*100/2300 = 28% i.e., option (d)

One might get confused in taking the base year and in such case if 2003 is taken the base year the candidate might mark option(c) 22% but that is the wrong choice.

Also, be sure about what is asked in the question, as if in confusion might misinterpret the question as if what is the percentage of total no. of products sold in 2003 wrt 2002, where numerator will 1300 and answer one will get is 128% i.e., option(b). Misinterpretation will also lead to​​ a​​ bad choice.

The second pitfall for a candidate​​ can be reading the data. Although in this sample problem units has been mentioned so you just have to add total no. of products and calculate percentage change, but in many cases, the units might not be mentioned and you just have to approximate the vale from bar height.​​ 

In such a case the readings are close to 1700 in 2002 and 2350 in 2003 as per bar height. Here the answer will be close to 35% but that too will lead to missing the right answer.​​ 

Here all the options are possible with​​ a​​ ​​ different interpretation of the question, so be careful of such traps in question.

  • What is the​​ approximate​​ percentage increase in​​ the​​ number of product A sold from 2001 to 2005?

(a)74% ​​  (b) 41%​​  (c) 140%(d) 46%

Solution:​​ As the​​ question clearly mention the percentage increase of product A from 2001 to 2005, we would take the difference in the number of product A sold in 2001 and 2005 and put it in numerator while keeping the base or denominator value as the number of product A sold in 2001.

​​ ​​ Percentage increase = (1125-800)*100/800 = 325*100/800 = 40.625% option(b)

In this​​ question also pitfall of take wrong denominator as 1500 gives option (a), taking assumed value if bar height gives option (d) and taking 1125(whole Product A not difference) ​​ as numerator would give option (b) but all these logical errors one must need to take care of because at the time of solving main paper a candidate under pressure is most likely to make these mistakes.

  • The​​ Number of Product​​ D​​ sold in​​ the​​ year 2004 is what per​​ cent of​​ the​​ number of product B and C sold together​​ in the same year? ​​ 

  • 77%​​  (b) 65%​​  (c) 147%​​  (d) 32%

Solution:​​ In this question, one needs to read carefully and deduce​​ 3 important points; first being the number of Product sold of​​ category D, second is​​ the​​ year​​ 2004​​ and third being​​ WRT Product category​​ B and ​​ C of​​ the​​ same year.

If you are keeping these 3 points in your then you won’t make the mistakes mentioned above.​​ 

Number of product D sold in 2004 = 570

Number of product B and C sold in 2004 = 740

Percentage od D wrt to B&C together = 570*100/740 =​​ 77%​​ option(a)

  • Composite Bar Graph

In simple or Stacked(component) bar chart only one kind of continuous variable can be represented in the form of different small component, one cannot represent multiple different continuous variables; in such a case a composite bar chart is used.

 

 

I hope given Example might have made​​ the​​ above explanation more clear but questions on this topic​​ are​​ similar to what we have done in stacked bar chart hence it will be covered in Practice Papers.

 

  • Deviation through Bar Chart

These bar charts are used when we have to represent both positive and negative values. Example of such variables can be Profit & Loss, Surplus & Deficit or Exports & Imports.

In this chart Baseline on X-axis would be the variable( Profit & Loss etc.) where the positive values(Profit in this case) are on the upper side while the lower side would be representing negative values(Loss).​​ 

Questions on the same will be discussed in Practice papers.

 

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