Pie Chart

A pie chart is a circle graph divided into pieces, each displaying the size of some related piece of information. Pie charts are used to display the sizes of parts that make up some whole. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk

While the pie chart is perhaps the most ubiquitous statistical chart in the business world and the mass media, it is rarely used in scientific or technical publications. It is one of the most widely criticized charts, and many statisticians recommend to avoid its use altogether. (Source of above paragraph: wikipedia)

Let s first try to put the similar set of data we have used in other charts. Say in CAT07 the number of questions asked from different chapters are
Algebra : 6 Geometry: 9 Number System:12 and Others: 3 and the total number of questions in math section is 30.

So algebra part consist of 6/30 x 100 = 20% of total questions. And similarly
Geometry: 30%
Number System: 40% and
Others: 10%

While representing the above numbers in a pie (circle) we ‘ll allocate the area(and thus the angle) to each section in such a way that each section’s percentage value corresponds to the equivalent area in the pie. And we ll get a chart as shown below.

You must be clear about how to make a pie chart. Now we will do the reverse – try to find information from a given pie chart (which is exactly what you ‘ll be doing in exam)

The below pie chart shows a typical Dhoni’s ODI innings. The numbers shows how many runs he has scored in single , twos, threes , fours and sixes.

After analyzing the above pie chart, try to answer the following questions:
1. What percentage of runs dhoni scored with threes
2. How many runs he had scored with boundaries (Note : both 6 and 4 are considered as boundaries)
3. What is the angle made by the sector representing runs scored in singles?
4. How many 6s he had hit in that innings

From the graph Dhoni has scored 9 runs with threes i.e 3 threes and the total run he has scored in that particular innings is 123.
So the percentage of runs Dhoni scored in 3s is 9/123 x 100 = 7.3%

Answer 2: Total runs scored in boundaries = 54 + 28 = 82

Answer 3: Total runs scored in single is 8 and that is 8/123 x 100 = 6.5% of the total run.
So the angle made is (6.5/100) x 360 = 23.41 degree

Answer 4: Total runs in 6s =54 so number of sixes is 54/6 = 9

Chart Comparison

Pie charts are generally not recommended to visualize information instead use bar- or line chars if the quantities are important.

Studies have shown that pie charts are hard to read if you actually have to answer questions about the numbers they represent. They look very pleasing and are used in a lot of places but they do not help to visualize information that well. Analytic thing person will read the percentages or values given on the legend or the chart it and analyze them in their head.

This is mostly because differences in angles are not easy to judge
For the human eye and there are a bunch of cases were you make the pie chart experience even worse. There are still reasons to use pie charts.

Example 1:

Answer the following questions with reference to the above pie chart

Q1. Of every dollar received by the federal government, how much (in cents) is from coporate sources?
A. 32
B. 70
C. 30
D. 35
E. 29
Answer : 1

Q2. what percentage of the federal revenue is derived from borrowings?
F. 0.2%
G. 0.02%
H. 2.7%
I. 1.2%
J. 2.5%
Answer : 3

Example 2:
Chart 1 shows the distribution of twelve million tonnes of crude oil transport through different modes over a specific period of time. Chart 2 shows the distribution of the cost of transporting this crude oil. The total cost was Rs. 30 million.

1.What is the cost of transporting petroleum by rail (in Rs)?
1. 2.5
2. 3.33
3. 6.4
4. 8

2.If the cost per tonne of transport by ship, air and road are represented by P, Q and R respectively, which of the following is true?
1. R > Q > P
2. P > R > Q
3. P > Q > R
4. R > P > Q

3. The cost in rupees per tonne of oil moved by rails and happens to be roughly
1. 3
2. 1.5
3. 4.5
4. 8

4. From the charts given, it appears that the cheapest mode of transport is:
1. Road
2. Rail
3. Pipeline
4. Ship

5.Which is the most effective way of transportation?
1.Road
2. Ship
3. Pipeline
4. cannot be determined

6.If for some reason ship stop sailing, by what percentage the airfreight have to go up to reach the previous level of volume transported (approximately)?
1. 75%
2. 81%
3. 85%
4 .90%

If the revenue after selling the petroleum was Rs 40 Million and other costs (including oil extraction, marketing etc) is Rs 5 Million, answer the following.

7.What is the Profit percentage?
1. 10%
2. 12.5 %
3. 15%
4. 20%

8. If the cost of transportation rises by 20 % and so does revenue,what is the margin %?
1. 14.08
2. 14.28
3. 14.58
4. 14.78

9.If all costs rise by 10% and revenue remains same ,what would be the decrease in percentage profit?
1. 35
2. 50
3.70 4 .80
10. If the pipeline cost increases by 30% ,by what percentage would revenue have to be increased so as to have same amount of profit?
1. 11.5
2.12.8
3.13.75
4. 14.6

11. If the govt includes a 15% tax on transportation costs ,what would be the effective cost per tonne of petroleum so as to have the same amount of profit as before?
1. 3.2
2.3.5
3.3.7
4. 4.2

1. 2. We get 3.6/1.08=3.33
2. 3 Calculate the cost by ship, air and road.
P = 3/1.08 = 2.77; Q = 2.10/1.32 = 1.58; R = 1.80/2.64 = 0.68 hence P > Q > R
3. 1 3.60/1.08 = 3.33
4. 1 Road is the cheapest, from Q 132.
5. 4 cannot be determined as e do not know on what criteria
6. 2. Air freight is 11% .it would have to increase to 20% i.e. increase by 81.81%
7. 2. 12.5 %
8. 3. 14.58 profit of 7 Million on revenue of 48 Million
9. 3. 70 %
10.4. Pipeline cost is 65%ie 19.5 Million. If this rises by 30 %, it rises by 5.85 Million .to offset this, Revenue would have to rise by the same amount, so 100 = 14.625%
11. 3. 3.7

Example 3:

Answer the following questions with reference to the above pie chart

Q1. What fraction of Ghosh babu’s weight consists of muscular and skin proteins?

(a) 1/13
(b) 1/30
(c) 1/20
(d) Cannot be determined

Q2. Ratio of distribution of protein in muscle to the distribution of protein in skin is:
(a) 3 : 1
(b) 3 : 10
(c) 1 : 3
(d) 3(1/2): 1

Q3. What percent of Ghosh babu’s body weight is made up of skin?
(a)0.15
(b) 10
(c) 1.2
(d) Cannot be determined

Q4. In terms of total body weight, the portion of material other than water and protein is
closest to:
(a)3/20
(b)1/15
(c)85/100
(d) 1/20

ANSWERS 1.(c) 2.(a) 3.(d) 4.(a)

Example 4:
The following pie charts give the percentage distribution of different types of employees in different departments, A, B, C, D and E.

1. What was the difference in total number of people in department A in 1999 and 2000?
(1)840
(2) 400
(3) 440
(4) 240

2. In the case of which department was there a maximum variation between 1999 and 2000?
(1)E
(2)B
(3)D
(4) A

3. If 300 employees left in department B at the end of 1999, how many people joined in this department in 2000?
(1) 340
(2) 460 (3) 980
(4) 1360

4. The number of employees in department D in 2000 is how many times the number of employees in department E in 1999?
(1) 3.5
(2) 2.8
(3) 2.33
(4) 1.77

5. What is the percentage increase in the number of employees in department C in 1999- 2000?
(1) 2%
(2) 2.34%
(3) 23.45%
(4) None of these

6. If the average monthly salary of employees in department A in 1999 was Rs 4,000, what was the annual salary bill for department A in 1999?
(1) Rs 19 lakh
(2) Rs 19 crore
(3) Rs 22 crore
(4) Rs 22 lakh

7. If the average salary for the whole company remained same in 1999 and 2000 at the level of Rs.5,000 per month, what was the percentage increase in the salary bill for the company in the two years?
(1) 4%
(2) 8%
(3) 9%
(4) 11%

ANSWERS:
1. 1 22% (18000) - 24% (20,000)
2. 3 Visually, we see D has the maximum variation.
3. 4 26% (20,000) = 23% (18,000) + 300
4. 2 20% (20,000)/8% (18,000)
5. 3 18% (18,000) to 20% (20,000) = 23.45%
6. 2 22% (18,000) 4000.
7. 4 (20 - 18)/18 = 11%

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