1. Introduction
Pie charts are specific types of data presentation where the data is represented in the form of a circle. In a pie chart, a circle is divided into various sections or segments such that each sector or segment represents a certain proportion or percentage of the total.
In such a diagram, the total of all the given items is equated to 360 degrees and the degrees of angles, representing different items, are calculated proportionately. The entire diagram looks like a pie and its components resemble slices cut from a pie. The pie chart is used to show the break-up of one continuous variable into its component parts.
For example, chart below shows the distribution of the sales of the car industry between six car companies.
Looking at the chart below, we can infer that Maruti accounts for 24 per cent of the market share, while GM accounts for 35 percent of the market share, Ford for4 percent of the market share, Tata for 10 percent of the market share, Hyundai for 15 percent of the market share and Fiat for 12 per cent of the market share.
Distribution of car sales between six companies
The pie chart encompasses a circle of 360 degrees which represents 100 per cent of the value of the continuous variable. Thus, 3.6 degrees on the pie chart represent 1 percent of the total value of the continuous variable being represented.
A single pie diagram can represent only one continuous variable. Hence, in terms of versatility of data representation, pie charts are less versatile than either of bar charts, x-y graphs or tables. However, their utility is in the fact that the representation of data is cleaner and it gives an immediate idea of the relative distribution of the continuous variable amongst different sectors.
Example Below will make the things easier to understand.
Example 1
Consider the information provided in the pie chart below relating to India's foreign trade in 1997-98 and the first eight months of 1998-99. Total trade with a region is defined as the sum of exports to and imports from that region.
Trade deficit is defined as the excess of imports over exports. Trade deficit may be negative.
Example 1.A
What is the region with which India had highest total trade in 1997-98?
(A) USA
(B) Other E.U.
(C) OPEC
(D) Others
Answer - (C)
Solution:
Trade with a region is the aggregate of imports from and exports to that region. The question is about a relative position and not an absolute position and thus should involve nothing more than glancing the pie charts and at the very most some small additions that can eminently he done orally. Whatever he the figures of total exports and total imports, these will not be necessary since what is asked is a relative position.
In the present case, imports into India are USD 40779 million and we may safely take I as 4 (rounding off 40779 to the nearest ten thousand) and exports from India are USD 33979 million we may safely take E as 3 (rounding off 33979 to the nearest ten thousand).
Option C is the clear choice. It would be stupid to merely add the percentages alone. A percentage is after all so much out of the whole. If you are comparing percentages of the same whole, you can tell which is higher. But comparing differing percentages of two different wholes is logical only when you take their absolute values. For Example 9% of 200 (we shall call 200 as A) is far higher than 36% of 40 (we shall call 40 as B) and rushing to the conclusion that 36% of B is higher than 9% of A would be stupid.
Assuming 40779 as 4 and 33979 as 3 would:
(A) Save a lot of time.
(B) Save a lot of effort..
(C) Ensure that we are comparing equals on both sides, and
(D) Ensure that you get the correct answer in a jiffy.
Question 1:In 1997-98 the amount of Indian exports, in millions US $, to the region with which India had the lowest total trade, is approximately:
Explanation
Others occupy 1% of the pie in both imports and exports and is the area with the lowest total trade. Indian exports aggregate roughly 34000 million and 1% of this is two zeroes off from 34000 and would mean 340. Thus Option B.
Question 2:In I997-98, the trade deficit with respect to India, in billions of US $, for the region with the highest trade deficit with respect to India, is approximately equal to:
Explanation
Let us assume that total imports are 100I and total exports are 100E. In case of one region - Region 1 - the imports are A% and exports are B% and in region 2 imports are C% and exports are D%. Trade deficit in Region 1 is (AI-BE) and in Region 2 it is (CI-DE).
If Trade deficit in Region 1 is higher than in Region 2, then (AI-BE)-(CI-DE) should yield a positive difference and this means that (AI-BE)>(CI-DE). If you subtract CI to both sides and add BE to both sides, you would get:
(AI-CI)>(BE-DE) or I(A-C)>E(B-D)
We know that I is greater than E in any case.
If (A-C) is greater than (B-D) the matter is clinched because then I(A-C) is indeed > E(B-D) and thus Trade deficit in Region 1> Trade deficit in Region 2.'
After all, (A-C) is some number and (B-D) is some other number. So (A-C)% of a higher base is bound to be higher than (B-D)% of a lower base so long as (A-C)>(B-D). This is utter logic. This logic is what is at test here.
In the present case, in all regions except OPEC and other East Europe, exports percentages are either more than or equal to imports percentages. We have to thus compare only OPEC and other East Europe and see whether (Difference in percentages of imports)> (Difference in percentages of exports).
In the case of OPEC and other East Europe (Difference in percentages of imports)=(23-19) and (Difference in percentages of exports)=(10-10) and hence (Difference in percentages of imports)>(Difference in percentages of exports) and thus trade deficit in OPEC is highest.
The trade deficit in this case works out to (0.23 ∗ 41-0.1 ∗ 34) = 9.2 -3.4 = 5.8 roughly.
Thus Option A: 6 billion.
Question 3:What is the region with the lowest trade deficit with India in 1997 - 98?
Explanation
The lowest trade deficit can also means a negative trade deficit or trade surplus. In case of the earlier question we have seen that Other EU has the second highest trade deficit and thus it is not a likely candidate for the least trade deficit. Hence we cross out Option D.
In USA and Asia we have trade surplus. In case of others there is a deficit. When we have trade surpluses, then we are to ignore trade deficits because a trade surplus is a negative trade deficit. So Option C is to be crossed out as well. We are now left with Options 1 and
As we have seen in the earlier question, if (Difference in percentages of imports) is greater than (Difference in percentages of exports) than Trade deficit in Region 1 > Trade deficit in Region 2. Now if we are to compare USA with Asia,
(Difference in percentages of imports) =(9 - 14)= -5 and
(Difference in percentages of exports)=(19 - 20)= -1.
Since -5 is not higher than -1, the trade deficit in USA is lower than the trade deficit in the case of Asia and hence Option A.
Question 4:Assume that the average monthly exports from India and imports to India during the remaining four months of 1998-99 would be the same as that for the first eight months of the year. What is the region to which Indian imports registered the highest percentage growth between 1997-98 and 1998-99?
Explanation
Look at the pie chart for exports in 1997-98, which is for a full year and for 1998 99, which is for eight months only.
As per the additional information, we are to assume that the average monthly exports from India and imports to India during the remaining four months of 1998-99 would be the same as that for the first eight months of the year.
If for eight months, the total exports have been 21436 million, the remaining four months (which is half of eight months) would have brought about an additional export equal to half of 21436 million, which is 10718 and the total exports would then have been 32154 million.
Since we are to state a comparative position - growth rate in exports in 1997-98 and exports in 1998-99, we can safely ignore the millions.
11% of 100 is less than 9% of 200 and so also 11% of I00 Billion is less than 9% of 200 Billion. What is the need for these millions while stating which is greater?
Secondly, if you are to compare between growth in exports over base yeah then you must appreciate that exports in 1998-99= exports in 1997-98 + growth in between/exports in 1997-98 = 1+ growth in between/exports in 1997-98 and thus when you compare the exports of two different regions, you can safely take the exports in the next year as a fraction of the base year instead of finding the difference between the exports in an year and the exports in the base year because when you compare the exports figures of Region 1 with that of Region 2 instead of incremental exports, you will get 1 on both sides of the comparison like this:
[1+ growth in between of exports in Region 1/exports in 1997-98] compared with [1+ growth in between of exports in Region 2/ exports in 1997-98], and if you strike off the 1 on both sides what you are really comparing is:
[Growth in between of exports in Region 1/exports in 1997-98] with [Growth in between of exports in Region 2/exports in 1997-98] which is what you want.
Let us see the options.
Option A:
Other East Europe. 10% of 33979 has grown to 12% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of Other East Europe, exports in 1998-99/exports in 1997-98 = 12B/10A.
Option B:
USA, 19% of 33979 has grown to 23% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of USA, exports in 1998-99/exports in 1997-98 = 23B/19A.
Option C:
Asia, 20% of 33979 has grown to 19% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of Asia, exports in 1998-99/exports in 1997-98 = 18B/20A.
Now what we are required to do is to compare among 12B/10A, 23B/19A and 18B/20A and say which is largest. In that case, neither B nor A in the numerator and denominator respectively are necessary because if you multiply all three fractions by A/B then you get 12/10, 23/19 and 18/20 and yet the relative values of the three fractious will remain unchanged.
If you were to multiply three fractions - say - 1/2, 2/3, and 3/4 by one million in the numerator and five million in the denominator, will it alter the fact that 3/4 (as it will seem after all the multiplications) will remain the largest and 1/2 the smallest of these three fractions? See for yourself. The three fractions will respectively seem like this: 1 million/10 million, 2 million/15 million and 3 million/20 million and yet the last will be the highest and the first will be the lowest.
So what you are then comparing is 12/10, 23/19 and 18/20 in which 18/20 will have to be booted out since it is less than 1 and then we are left with 12/10 and 23/19. If we divide 12 by 10, we get 1.2.
If we divide 23/19 we get 1.2 till the first decimal and have to carry on to the next decimal and hence we get 1.21. We s here and declare that USA has highest growth among the three options and thus Option B is correct.
But there is a small googly here. Option D says that exports have declined or there has been no growth in any region. This has to be checked. We know that the highest percentage growth is in the case of USA. But percentage growth is about relative growth whereas the Option D talks about absolute growth. Whether there has been no growth or decline in absolute terms can be ascertained from only absolute figures.
Now see the utter logic in this. If this logic goes home, you will be saved a huge lot of calculations. Logic is the name of the game and even if it takes some time for this simple logic to register, it is recommended that you should absorb the fundamentals.
Since we know that in case of USA the percentage growth rate has been highest, we may just see whether there has been actual growth in this case (we shall choose the highest percentage growth rate to check because if there has not been absolute growth where the percentage growth is highest, then in cases of lower percentage growth, the likelihood of an absolute growth is zero).
In case of USA, export percentage grew from 19% of 33979 million to 23% of 32154 million. For determining whether there was growth, the millions are unnecessary once again. They would be needed if you were asked how much was the growth.
But even then, if the answer is to be given in millions, the millions become redundant once again. Give these millions a well-earned rest. Round off 33979 to 34 (forget the thousands as well) and round off 32154 to 32 (forget the thousands here as well) and see whether 19% of 34 is less than 23% of 32. You will find that so exports have indeed grown in the case of USA at least and hence Option D (which if true would mean that there has not been any growth in exports in any region) does not hold water.
So Option B.
Question 5:Assume that the average monthly exports from India and imports to India during the remaining four months of 1998-99 would be the same as that for the first eight months of the year. What is the percentage growth rate in India's total trade deficit between 1997-98 and1998-99?
Explanation
lndia’s trade deficit in 1997-98 in USD billions is:
40.7-33.9=6.8
In 1998-99, it is (28.1 ∗ 1.5) - (21.4 ∗ 1.5)=42.15 - 32.1 = 10.05
The trade deficit has gone up from 6.8 billion USD by 3.25 billion USD to 10.05.
This increase of 3.25 as a percentage of 6.8 is:
From among the options 47% seems to be the answer. So Option B: 47%.
