*Monday, February 18th, 2019*

Data Interpretation holds an inevitable place in todayâ€™s world. Everything revolves around the data. Itâ€™s being continuously collected, structured and then meaningful conclusions are drawn from it after careful research and analysis. Thus, data is important but itâ€™s useless without its accurate interpretation and thatâ€™s why Data interpretation is included as a section in various competitive exams especially MBA entrance exams such as CAT, XAT, IIFT, SNAP etc. In these exams, data will be represented in various formats such as graphs, charts, tables etc. along with 3-4 questions that will be based on the structured data. To excel in this section, you not only need knowledge of various forms of data representation techniques and formats like graphs and charts but also basic arithmetic formulas and concepts of percentages, ratios etc. This article is strictly concentrated on one specific form of data representation format that have been asked in exams known as **Pie Charts**.

Pie Charts are the circular way of data representation. In these graphs, a circle is divided into various segments and each single segment denote a category from the given data. In a pie chart, theÂ arc lengthÂ of each slice (and consequently itsÂ central angleÂ andÂ area), isÂ proportionalÂ to the quantity it represents. Pie graphs use percentage or angles to show relative sizes of various categories. Pie charts can be used in following ways.

- They are a visual way of displaying data that might otherwise be given in a small table.
- Pie charts are useful for displaying data that are classified into nominal or ordinal categories. Nominal data are categorized according to descriptive or qualitative information such as county of birth or type of pet owned. Ordinal data are similar but the different categories can also be ranked, for example in a survey people may be asked to say whether they classed something as very poor, poor, fair, good, very good.
- They are generally used to show percentage or proportional data and usually the percentage represented by each category is provided next to the corresponding slice of pie.
- They are good for displaying data for around 6 categories or fewer. When there are more categories it is difficult for the eye to distinguish between the relative sizes of the different sectors and so the chart becomes difficult to interpret.

There are various kinds of pie graphs namely, 3D pie chart, doughnut chart, exploded pie chart, ring chart etc. But in the exam, we will usually be given the basic pie chart which is given below.

Letâ€™s now solve a couple of questions to understand how to use data given in form of pie graphs. First understand one more point before solving questions.

A circle is of 360^{o} and this 360^{o} represent the total value of the data that chart represents. So, if letâ€™s assume the total sale is of 10,000 then 360^{0Â }represent 10000. And each segment in the pie chart either given in form of an angle or percentage represent a portion of total value. So, to quickly solve the questions you need to know a few things i.e. the value of each segment in actual form and the total sum of all the values. Also, you need to know the conversion between degrees and percentages. I will let you know the formula later when required in any question though itâ€™s easy and you can do it yourself as well.

**Example 1: **The following pie chart shows the amount of subscription generated for Indian Bonds from different categories of Investors.

**Question 1**: If the investment by NRIâ€™s are INR 4,000 crore, then investment by both corporate houses and FIIâ€™s together is:

a.) 24000 crores

b.) 24363 crores

c.) 25423.4 crores

d.) 25643.3 crores

**Question 2**: What percentage of total investment is coming from either FIIâ€™s or NRIâ€™s?

a.) 33%

b.) 44%

c.) 11%

d.) 22%

**Question 3**: If the total investment other than by FII and corporate houses is INR 335,000 crore, then the investment by NRIâ€™s and offshore funds will be (approximately):

a.) 274,100

b.) 285,600

c.) 293,000

d.) Cannot be determined

**Question 4**: What is approximate ratio of investment flows into India Bonds from NRIâ€™s to corporate houses?

a.) 1:4

b.) 1:3

c.) 3:1

d.) Cannot be determined

**Question 5**: In corporate sector, approximately how many degrees should be there in the central angle?

a.) 120

b.) 121

c.) 122

d.) 123

**Question 6**: If the total investment flows from FII were to be doubled in the next year and the investment flows from all other sources had remained constant at their existing levels for this year, then what would be the proportion of FII investment in the total investment flows into Indian Bonds in the next year (approximately)?

a.) 40%

b.) 50%

c.) 60%

d.) 70%

**Question 7**: If the flow from the FIIâ€™s after the doubling (of previous question) were to the tune of US$ 500 million, what would be the total investment into Indian Bond in US $â€™s?

a.) 1000

b.) 1500

c.) 800

d.) Cannot be determined

**Solution: **

**Ans 1:** If the investment by NRI is worth 4000 crores which is 11% of total value.

Then, the total value will be = **4000 * 100/11**

= 36363.63

Now, investment by corporate houses and FIIâ€™s together will be 67% of 36363.63 i.e. **24,363.63 crore**.

**Ans 2**: This is a very direct question and the answer is 44%

**Ans 3**: This question will be solved in similar manner like the question 1.Â The investment other than by FIIâ€™s and corporate house is total is-s 33% amounted to 335,000 crores.

Then total investment by everyone will be **335,000 * 100/33**

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **= 1015151.5151

And NRIâ€™s and offshore funds constitute 27% of total investment. Hence, **0.27 of 1015151.5151 **i.e. **274,090.90**.

**Ans 4: **Again, this one is simple one. The investment by NRIâ€™s is 11% and corporate house is 34%. Therefore, the ratio will be **11:34** i.e. approximately **1:3**.

**Ans -5**: To solve the question you need to learn how to convert percentage into degrees and itâ€™s pretty simple. You just need to multiply the percentage with 360^{o} i.e. **11/100 * 360 ^{o} **=

Now in this question, we need to find the central angle of corporate house i.e. **0.34** of **360 ^{o}** i.e.

**Ans 6**: The current FIIâ€™s are 33% and it will double next year making it 66%. Thus, keeping other investment constant now the total becomes 133.

Hence, 66 % of 133 will be **49.62% **i.e. **50%**.

**Ans 7: **500 million is 50% of the total investment as we found in the previous question. Thus, total investment will be **500 * 100/50 i.e. 1000 million dollars**.

**Â **

**Example 2**: Study the following diagram carefully and answer the questions:

Percentage Composition of Human Body

**Question 1**: What percent of the total weight of human body is equivalent to the weight of the proteins in skin in human body?

a.) 0.016

b.) 1.6

c.) 0.16

d.) Cannot be determined

**Question 2**: What will be the quantity of water in the body of a person weighing 50 kg?

a.) 20 kg

b.) 35 kg

c.) 41 kg

d.) 5 kg

**Question 3**: What is the ratio of the distribution of proteins in the muscles to that of the distribution of proteins in the bones?

a.) 1:18

b.) 1:2

c.) 2:1

d.) 18:1

**Question 4**: To show the distribution of proteins and the other dry elements in the human body, the arc of the circle should subtend at the center an angle of;

a.) 54^{o}

b.) 126^{o}

c.) 108^{o}

d.) 252^{o}

**Question 5**: In the human body, what part is made of neither bones nor skin?

a.) 1/40

b.) 3/80

c.) 2/5

d.) None of these

**Solution 2**:

**Ans 1**: Now to solve this question you have to make use of both the pie charts. Since, total percentage of protein in body is 16%. And, the total percentage of weight of skin in human body is 10%. Therefore, the percentage of protein in skin is **10% of 16**.i.e. **1.6**.

**Ans 2**: Water constitutes 70% of the body. Thus, if the man weighs 50 kg then 70% of it will be water. The weight of water will be **35 kgs.**

**Ans 3**: Again, using both pie charts we know that 33% of body weight is constituted in muscles where as 17% in bones and 16% of it will be protein.

Hence, **0.16*33**:** 0.16*17**, which is approximately equal to **2**:**1**.

**Ans 4**: Using the formula given in the example 1, Ans 5 we get,

**[(16% + 14%)/100] * 360 ^{o} **=

**Ans 5**: Now let u-s consider the body to be- numeraire as 1 and 17/100 and 10/100 constitutes bones and skin respectively i.e. 1/6 and 1/10

Hence, the requires answer is **1 â€“ (1/6 +1/10) **= **11/15**.

**Â **

**XAT 2012**: The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.

**Question 1**: If the batsman has scored a total of 306 runs, how many 4â€™s and 6â€™s did he hit?

a.) 31 and 3 resp.

b.) 32 and 2 resp.

c.) 32 and 3 resp.

d.) 33 and 1 resp.

e.) 33 and 2 resp.

**Question 2**: If 5 dot balls had been hit for 4s, and if two of the shots for which the batsman scored 3 runs each had fetched him one run instead, what would have been the central angle of the sector corresponding to the percentage of runs scored in 4s?

a.) 160

b.) 163

c.) 165

d.) 167

e.) 170

**Solution 3**:

**Ans 1**: Total runs scored by batsman is 306. % of 4â€™s and 6â€™s hit by him are** 43 **and **4 **respectively.

Thus, there were 0.43 * 306/4 and 0.04 * 306/6 were 4â€™s and 6â€™s resp.

**i.e., 33 and 2**.

**Ans 2**: Since, the total runs scored by batsman is 306 and therefore total no. of runs secured through 4â€™s are **0.43 **of **306** i.e. 132. Now if, 5 more fours are added to it the total becomes 152.

Now the overall total runs secured by batsman after adding 5 fours and deducting 2 threeâ€™s and simultaneously adding 2 oneâ€™s is **306 +16 **= **322**

The central angle for 4â€™s would be **152**/**322 *** **360** = **170**^{o}.

**SNAP 2005**: Study the sector wise sales of a group of companies for the financial year 2004-05 and answer the following question:

Sectors |
(Rs. Millions) |
% Share |

Materials |
164,430 | 21.0 |

Engineering |
244,830 | 31.2 |

Energy |
62,990 | 8.0 |

Consumer goods |
47,880 | 6.1 |

Chemicals |
35,510 | 4.5 |

Communication and Information system |
148,160 | 18.9 |

Services |
78,950 | 10.1 |

Total |
782,750 | |

*Sales turnover at US$ 17.4 billion (Rs. 78,224 crore) representing a year-on-year growth of 30.3 % in dollar terms and 27.4 % in rupee terms. |
||

*sales figures shown are net of excise duty |

**Question 1:** This group of companies operates in multiple sectors. The holding company has decided to closely monitor minimum number of sectors (not exceeding 5) contribution together a major part (at least 80%) of sales of the group. Identify the correct set of sectors.

a.) Engineering, Services, CIS & Consumer Goods

b.) Engineering, Services, CIS, Energy & Consumer Goods

c.) Engineering, Materials, Services & CIS

d.) Engineering, Materials, CIS & Energy

**Question 2:** The average profit against the sales across the sectors is 10% while the profit margin of Engineering is 12% and CIS, 20%. What is the average profit across the remaining sectors?

a.) 5.87%

b.) 6.12%

c.) 4.94%

d.) 4%

**Solution:**

**Ans 1**: The solution to this question is very easy. Just use the pie chart and add the highest 4 contributing sectors i.e. **Engineering, Materials, CIS, Services**. Their total is

(33+21+19+10) is 91% i.e. more than 80.

**Ans 2**: Total sales = **782,750**.

Average profit = 10% i.e. **78,275**

Profit of engineering and CIS respectively are **12**% of **244,830** and **20% **of **148,160** i.e. **29,379.6 **and **29,632.**

**Â Â Â Â Â Â Â Â Â Â Â **Hence, the profit of remaining sectors is **78,275** â€“ **59,011.6 **= **19,263.4**

**Â Â Â Â Â Â Â Â Â Â Â **Thus, % of average profit for rest of the sectors is (**19,263.4**/ **78,275**) * **100/5 **= **4.94**%

**CAT 2018****: **The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three-monthly sales figures in the fourth quarter (October, November, December) of that year**.**

1. What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?

a.) 38.46

b.) 22.22

c.) 50.00

d.) 28.57

2. In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?

a.) Q4

b.) Q1

c.) Q2

d.) Q3

3. During which quarter was the percentage decrease in sales from the previous quarterâ€™s sales the highest?

a.) Q2 of 2016

b.) Q2 of 2017

c.) Q4 of 2017

d.) Q1 of 2017

4. During which month was the percentage increase in sales from the previous monthâ€™s sales the highest?

a.) October of 2017

b.) October of 2016

c.) March of 2016

d.) March of 2017

**Solution:** To easily solve the questions we can first represent the information given in pie-chart in a consolidated table to make it easier to read and understand.

Month/ sales figure in | 2016 | 2017 | |

Q1 | January | 80 | 120 |

February | 60 | 100 | |

March | 100 | 160 | |

Q2 | April | 40 | 60 |

May | 75 | ||

June | 65 | ||

Q3 | July | 75 | 60 |

August | 120 | ||

September | 55 | 70 | |

Q4 | October | 100 | 150 |

November | 170 | ||

December |

As you can see in the above table there a few monthâ€™s sales are missing and we need to evaluate them first from the given information and then find the answers to above given question.

Now, itâ€™s been given in the question that the months of April, May, June in 2016 forms an A.P. and so does the months of Quarter 4 of 2016, i.e. Oct, Nov, Dec.

Total sale in Quarter 2 = 150

Let a-d, a, a+d be the three terms of A.P.

Hence, **a-d + a + a+d** =**150**

**3a**=**150****a**=**50**

Since, April sale is 40, i.e. **a-d** = **40**

**d**=**10**

Using that we can easily find the rest of the month sales values i.e. 50 and 60 respectively.

Similarly, using the above method we can find out the values for month of Novâ€™16 and Decâ€™16. In this case, a would be 120 and d = 20.

Thus, sales for these months are 120 and 140 respectively.

Now as you can see in the table, we have found out all missing monthly sales figure except for Decemberâ€™17 and Augustâ€™17 which can be easily find out as

Total sales in Quarter 4 of 2017 = 500

And sales in Octâ€™17 and Novâ€™17 are 150 and 170 respectively.

Hence, the sale for December =** 500 -150-170 **

= **180**

And similarly, Sale for Augustâ€™17 = **220 â€“ 60 â€“ 70** = **90**

Therefore, our table becomes,

Month/ sales figure in | 2016 | 2017 | |||

Q1 | January | 80 | 240 | 120 | 380 |

February | 60 | 100 | |||

March | 100 | 160 | |||

Q2 | April | 40 | 150 | 60 | 200 |

May | 50 | 75 | |||

June | 60 | 65 | |||

Q3 | July | 75 | 250 | 60 | 220 |

August | 120 | 90 | |||

September | 55 | 70 | |||

Q4 | October | 100 | 300 | 150 | 500 |

November | 120 | 170 | |||

December | 140 | 180 |

Now we are in position to answer all the given questions using the above table.

**Ans 1**: Percentage increase in sales of Decâ€™17 as compared to Decâ€™16 =

**Ans 2**: We need to evaluate the quarter with the highest increase in sales in percentage terms.

Quarter | Increase in sales | Percentage terms |

Q1 | 140 | 58.333% |

Q2 | 50 | 33.333% |

Q3 | (30) | (12%) |

Q4 | 200 | 66.67% |

Hence, using the above table we get the answer is Quarter 4

**Ans 3**: As we can clearly notice above from the table that the decrease in sales is only in quarter 2 of both the years 2016 and 2017.

Decrease in Q2- 2016 **= **

Decrease in Q2- 2017 =

Hence, the answer is Quarter 2â€™2017

**Ans 4**: In this question you donâ€™t need to find the percentage rise for all the months as you can clearly notice in the options that comparison is given only for march and October 2016 and 2017. Thus, find out the percentage rise for these months and you are done.

Also, notice that the rise in sales for Octoberâ€™17 is highest compared to Sepâ€™17. The sale got more than double from 70 to 150. Hence, Octoberâ€™17 answer is the correct answer.

As the above examples depict the questions are pretty straightforward for pie charts. But I still recommend you to practice a good amount of questions to get fluent with this topic. So, keep Practicing!

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