Data Interpretation - Pie charts


Basics:  
Total angle at the center of a pie chart = ${360^0}$
To convert k% percentage into angle = $\displaystyle\frac{k}{{100}} \times {360^0}$
To convert ${m^0}$ into percentage = $\displaystyle\frac{m}{{360}} \times 100$

Set 1 : The various sections of the population are indicated below in the pie-chart. Study the pie-chart and answer the following questions:
The total population of a city is 5000
I.  Employees of the Public Sector II. Employees of the Private Sector
III. Employees of the Corporate Sector IV. Self-Employed   V. Unemployed.

1. What percentage of the employed persons is self employed?
a.   5%b.  5 5/19 %c.  19%d.  20%
Solution:  Total Employed = Total population - Unemployed = ${360^0} - {18^0} = {342^0}$
Now self employed are ${18^0}$. So self employed as a percentage of employed = $\displaystyle\frac{{18}}{{342}} \times 100 = 5\displaystyle\frac{5}{{19}}\% $

2. Number of persons employed in the Corporate Sector is 
a.   250b.  500c.  750d.  1500
Solution: We have to convert degrees into numbers.  So $\displaystyle\frac{{54}}{{360}} \times 5000 = 750$

3. The number of Unemployed persons is 
a.   250b.  150c.  100d.  50
Solution: We have to convert degrees into numbers. So $\displaystyle\frac{{18}}{{360}} \times 5000 = 250$
Shortcut: We calculated corporate sector employees as 750. But from pie chart Corporate sector employees are 3 times of unemployed. So 1/3rd of 750 = 250

4. The number of persons employed in both the Public Sector and Corporate Sector is 
a.   3750b.  3000c.  2500d.  2200
Solution: Number of persons employed in public sector and corporate sector together = 54 + 162 = 216.
$\displaystyle\frac{{54 + 162}}{{360}} \times 5000 = \displaystyle\frac{{216}}{{360}} \times 5000 = 3000$

5. What percentage of the employed persons is employed in Private Sector ?
a.   29%b.  31 11/19%c.  34%d.  31%
From the 1st question, employed are 342. and From pie chart private sector employees are 108.
$\displaystyle\frac{{108}}{{342}} \times 100 = \displaystyle\frac{{600}}{{19}} = 31\frac{{11}}{{19}}\% $

Set 2:  These questions are based on following graphs Classification of appeared candidates in a competitive test from different states and qualified candidates from those states.


1. What is the ratio between the number of appeared candidates from states C and E together and the appeared candidates from states A and F together ?
a.  17 : 33
b.  11 : 13
c.  13 : 27
d.  17 : 27 
Solution: There is not need to calculate values. This is simply a ratio. So we can compare the ratio of their percentages. C + E = 8 + 9 = 17; A + F = 15 + 18 = 33.

So ratio = 17 : 33




2. In which State the percentage of qualified candidates to that of appeared candidates is minimum ?
a.  C
b.  F
c.  D
d.  E
Solution:  This is a lengthy question. But we will use simple technique to solve this question.
We have to calculate the ratio of Qualified to appeared for each state. So $\displaystyle\frac{\text{Qualified candidates from A}}{\text{Selected candidates from A}} \times 100 = \displaystyle\frac{{18\%  \times 9000}}{{15\%  \times 45000}} \times 100$
But If you observe in the above equation, only 18% / 15% changes for each state. Remaining values are constant. Minimum percentage we get if numerator is small and denominator is big.
For C it is 7/8 = 1/1.14 and for E it is 9/14 = 1/1.5 So for E denominator is big. So it has the ratio Minimum.
So Option D is correct.

3. What is the difference between the number of qualified candidates of states D and G
a.   690b.  670c.  780d.  720
Solution: Instead of calculating qualified candidates for D and G separately, we take the difference in their percentages.  i.e., 8% (9000) = 720.

4. What is the percentage of qualified candidates to that of appeared candidates from states B and C taken together ?
a.   23.11b.  24.21c.  21.24d.  23
Qualified candidates from B and C = (16 + 7)% = 23% (9000)
Appeared candidates from B and C = (11 + 8)% = 19% (45000)
So required percentage = $\displaystyle\frac{{23\% (9000)}}{{19\% (45000)}} \times 100 = \displaystyle\frac{{23}}{{19 \times 5}} \times 100 = 24.21$

5. What is the ratio between number of candidates qualified from states B and D together and the number of candidates appeared from state C respectively ?
a.   8 : 37b.  11 : 12c.  37 : 48d.  7 : 37
Solution: The required ration = (16 + 21)% (9000) : 8% (45000) $ \Rightarrow $ 37 : 8 x 5 $ \Rightarrow $ 37 : 40