Bar Graph DI Tricks & Tips
Bar Graphs
Positives  Negatives 

1. Trends can be easily established as compared to tables and piecharts.  1. Less accurate than tables as at times, especially when the grid lines of the graph are missing because of which exact value of the bar cannot be accurately established. 
2. Comparative type questions can be easily solved by visual inspection of graph.  2. The graph may get a little complicated in case of multiple bar chart or stacked bar chart. 
Shortcuts to crack DI sets containing Bar Graphs
1. In comparison based questions use the lengths of the bar and not exact values to solve the questions visually.
Here is a CAT 2003 (Feb) DI set to illustrate the same.
It is clear that to solve the above question we need to look at the second graph. However, rather than struggling to get the exact values and then spending more time diving them to get the answer, we can do better by solving the question visually. The question boils down to diving the unshaded bars by the shaded ones and find out for which year would this value be the highest. For a fraction to be the highest, its numerator should be as high as possible and the denominator should be as low as possible. In other words, the unshaded bar should be as long as possible and the shaded bar should be as short as possible. This is clearly seen for the year 1995.
2. Use the grid lines effectively for quick calculations.
Let us solve this CAT 1996 question to understand the same.
One way to solve the above question is to add up the exact values and get the answer. The other way is to establish every value of the Revenue in terms of ‘Gridlines’. For example, in 1991, the value of Revenue corresponds to 5.75 gridlines. Similarly for 1992 it is 6.5, for 1993 it is 7.5, for 1994 it is 8 and for 1995 it is 8.75. If we were to add all, we get a value equivalent to 36.5 gridlines. Since we know every gridline corresponds to a value of 25 lakhs, every 4 gridlines would correspond to a value of 100 lakhs or 36 gridlines would correspond to a value of 900 lakhs. Plus another 0.5 grid lines corresponds to 12.5 lakhs. Thus the total revenue for the given 5 years is 912.5 lakhs.
This method helps you to deal with singledigit or twodigit values and hence enhance your calculation speed.
Reading Bar Graphs
 Three different bars represent three different games: Football, Cricket, and Badminton.
 On the Xaxis, we have a number of countries from 1 to 6.
 On the Yaxis we have the number of players.
 The length of the Bars denotes the number of players.
 177.77%
 176.78%
 178.87%
 180.82%
 335
 635
 435
 535
 134%
 164%
 126%
 157%
 Country 3 & 2
 Country 4 & 6
 Country 3 & 4
 Country 5 & 1
 127:170
 13:7
 49:27
 87:55
1. Use Approximation in Calculations
2. Effective Analysis of given Data
3. Catch the right Data
4. Become familiar with all types of Data
5. Skip Unnecessary Calculations
6. Accuracy is the key factor
7. Don’t use calculators while Practice
8. The key to success is Practice
Example: Questions on Bar Graph and Line Graph from Data Interpretation for IBPS PO and SSC CGL.
Problem:
Question 1: Approximately, what is the average population of state A for all the given years?
1) 65 lakhs 2)50 lakhs 3)48 lakhs 4) 58 lakhs 5) 52 lakhs
Solution:
Step 1:
Total population of State A = 410 Lakhs
Step 2:
Average Population of State A = Total population of State A / Number of Years
Step 3:
By substituting the values in the formula,
410/ 7 = 58.7
Therefore, The approx average population of State A is 58% – option 4.
Question 2: What is the ratio of the total population of state A for the years 2001, 2002 and 2003 together to the population of state B for 2005,2006 and 2007 together.
*Tip – We need to find ratios.
Solution:
Step 1:
As we need to find ratio,
^{State A }(2001 + 2002 + 2003) : State B(2005 + 2006 +2007)
Step 2:
By substituting the values in the above formula,
(40 + 45 + 60) : (80+ 90+100) (Substituting the values in the formulas)
Step 3:
By simplification,
= 145 : 270
= 29:54
Therefore the ratio of number of people in the state A( 2001 + 2002 + 2003)to the number of people in the state B( 2005 + 2006+ 2007) is 29 : 54
Question 3: What is the percentage rise in population of state B from the year 2003 to 2004?
*Tip: We need to find the percentage change
Solution:
Step 1:
As we need to find the percentage rise in the population, we use
Percentage Increase = [(final – Initial) /Initial] x 100
=Difference /Initial x 100
Percentage Increase = (Population of state B during 2004 – 2003/ 2003) x 100
Step 2:
By substituting the values in the formulas,
= [(70 – 60)/60 x 100]
=10/60 x 100
= 1/6 x 100
= 16.66%
Therefore, there has been a rise in 16.66% of population during the year 2003 and 2004 in State B.
Question 4: What is the difference in the total population of State A and total population for State B for all the years.
Solution:
Step 1:
As we need to find the total difference in the population of State A and State B, we can individually take the difference for each year and add all the differences to find the difference between total population of State A and State B.
Total A – Total B = Difference_{(First year) }, Difference_{(Second year) }Difference_{(Third year) }, Difference_{( Fourth year) }, Difference_{(Fifth year) }, Difference_{(Sixth year) }, Difference_{(Seventh year).}
Step 2:
By substituting the values in the above formula,
(10)+5+0+(20)+(10)+(25)+(20)
= 80 Lakhs
Therefore, The difference in their population is 80 lakhs.
Question 5:For which state and in which year , the percent rise in population from the previous year was the highest.
1) State B – 2003
2) State B – 2002
3) State A – 2004
4) State A – 2005
5) None of these
Solution:
State B – 2003:
Percent rise = Difference / Initial x 100
= (60 – 40)/40 x 100
= 20/40 x 100
= 50%
By using the formula, find out the percentage rise in population for both states respective to all the years and select the correct option.
Practice Set On Bar Graph DI
 In the following bar diagram the number of engineers employed in various companies has been given. Study the bar diagram carefully to answer the questions.
 If the number of all the engineers in the company V, company X and companyY be increased by 30%, 35% and 40% respectively, what will be the overall percentage increase in the number of all engineers of all the companies taken together?
A)18%
B) 22%
C) 30%
D) 35%
E) 42%  What is the average number of junior engineers employed in all the companies?
A) 150
B) 110
C) 170
D) 200
E) 190  If the number of assistant engineers employed in all the companies be increased by 37% and the number of post graduate engineers employed in all the companies be decreased by 20% by what per cent will the number of assistant engineers be less than that of post graduate engineers?
A) 13.52%
B) 17.72%
C) 19.87%
D) 22.15%
E) 15.42%  What is the ratio between the number of assistant engineers employed in company V and company X ?
A) 5 : 6
B) 3 : 4
C) 5 : 7
D) 2 : 3
E) 1 : 2  What is the difference between the average number of junior engineers and assistant engineers taking all the companies together?
A) 10
B) 50
C) 30
D) 20
E) 40
Study the following graph carefully to answer the questions that follow:
 What was the respective ratio between the number of students who qualified in the exam from school P in the year 2005 and the number of students who qualified in the exam from schoolQ in the year 2008?
A) 17 : 30
B) 15 : 28
C) 18 : 22
D) 17 : 18
E) 19 : 23  Total number of students who qualified in the exam from school –P over all the years together was approximately what percentage of total number of students who qualified in the exam from both the schools together in the years 2006 and 2007 together?
A) 129%
B) 130%
C) 147%
D) 150%
E) 144%  If 40% of the total students who qualified in the exam from both the schools together over all the years are females, then what was the total number of males who qualified in the exam over all the years from both the schools together?
A) 51000
B) 56000
C) 45000
D) 54000
E) 67000  What was the difference between the total number of students who qualified in the exam in the year 2005 from both the schools together and the total number
of students from schoolQ who qualified in exam over all the years together?
A) 252400
B) 214500
C)125700
D)150000
E) 30000  What was the approximate per cent increase in the number of students who qualified in the exam from school – Q in the year 2007 as compared to the previous year ?
A) 45
B) 50
C) 72
D) 64
E) 48
The bar graph given below shows the sales of books (in thousand number) from six branches of a publishing company during two consecutive years 2000 and 2001.
Sales of Books (in thousand numbers) from Six Branches – B1, B2, B3, B4, B5 and B6 of a publishing Company in 2000 and 2001.
2.  Total sales of branch B6 for both the years is what percent of the total sales of branches B3 for both the years?  
Answer: Option C Explanation:

3.  What percent of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?  
Answer: Option D Explanation: Average sales (in thousand number) of branches B1, B3 and B6 in 2000
Average sales (in thousand number) of branches B1, B2 and B3 in 2001

4.  What is the average sales of all the branches (in thousand numbers) for the year 2000?  
Answer: Option B Explanation: Average sales of all the six branches (in thousand numbers) for the year 2000
= 80. 
5.  Total sales of branches B1, B3 and B5 together for both the years (in thousand numbers) is?  
Answer: Option D Explanation: Total sales of branches B1, B3 and B5 for both the years (in thousand numbers) = (80 + 105) + (95 + 110) + (75 + 95) = 560. 
The bar graph given below shows the foreign exchange reserves of a country (in million US $) from 1991 – 1992 to 1998 – 1999.
Foreign Exchange Reserves Of a Country. (in million US $)
1.  The ratio of the number of years, in which the foreign exchange reserves are above the average reserves, to those in which the reserves are below the average reserves is?  
Answer: Option C Explanation: Average foreign exchange reserves over the given period = 3480 million US $. The country had reserves above 3480 million US $ during the years 199293, 199697 and 199798, i.e., for 3 years and below 3480 million US $ during the years 199192, 199394, 199495, 199556 and 199899 i.e., for 5 years. Hence, required ratio = 3 : 5. 
2.  The foreign exchange reserves in 199798 was how many times that in 199495?  
Answer: Option D Explanation:

3.  For which year, the percent increase of foreign exchange reserves over the previous year, is the highest?  
Answer: Option A Explanation: There is an increase in foreign exchange reserves during the years 1992 – 1993, 1994 – 1995, 1996 – 1997, 1997 – 1998 as compared to previous year (as shown by bargraph). The percentage increase in reserves during these years compared to previous year are:
Clearly, the percentage increase over previous year is highest for 1992 – 1993. 
4.  The foreign exchange reserves in 199697 were approximately what percent of the average foreign exchange reserves over the period under review?  
Answer: Option D Explanation: Average foreign exchange reserves over the given period
= 3480 million US $. Foreign exchange reserves in 1996 – 1997 = 4320 million US $.

5.  What was the percentage increase in the foreign exchange reserves in 199798 over 199394?  
Answer: Option A Explanation: Foreign exchange reserves in 1997 – 1998 = 5040 million US $. Foreign exchange reserves in 1993 – 1994 = 2520 million US $. Increase = (5040 – 2520) = 2520 US $.

The bar graph given below shows the data of the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years.
Production of Paper (in lakh tonnes) by Three Companies X, Y and Z over the Years.
1.  For which of the following years, the percentage rise/fall in production from the previous year is the maximum for Company Y?  
Answer: Option A Explanation: Percentage change (rise/fall) in the production of Company Y in comparison to the previous year, for different years are:
Hence, the maximum percentage rise/fall in the production of Company Y is for 1997. 
2.  What is the ratio of the average production of Company X in the period 19982000 to the average production of Company Y in the same period?  
Answer: Option C Explanation: Average production of Company X in the period 19982000
Average production of Company Y in the period 19982000

3.  The average production for five years was maximum for which company?  
Answer: Option D Explanation: Average production (in lakh tons) in five years for the three companies are:
Average production of five years is maximum for both the Companies X and Z. 
4.  In which year was the percentage of production of Company Z to the production of Company Y the maximum?  
Answer: Option A Explanation: The percentages of production of Company Z to the production of Company Z for various years are:
Clearly, this percentage is highest for 1996. 