Using Pie charts to solve arithmetic problems

In the last presentation, I introduced pie charts which is one of the tools used to represent and compare statistical data. I solved one example. If you missed that post, you may want to take a look at it here.

So in this second presentation, we will see further examples of how we can use pie charts to represent data and solve for some unknow quantity. Let us look at two examples now.

Example 1: The information below shows staff distribution in a bottling company. Use it to answer the questions that follow.

Data entry officers = 36
Drivers = 44
Receptionists = 78
Security officers = 30
Office assistants = 52

(a) Use a pie chart to represent the information
(b) How much will be the salary of data entry officers if the total salary of workers is $144,000
(c) What percentage of the workforce are security officers.
(d) What percentage of the salary is paid to drivers and office assistants?

Solution

(a) Use a pie chart to represent the information
The first step is to workout the size of each sector in a table. Remember that a pie chart - which is a circle - has its size equal to 360^o. So below is the table.

Table of scores and sectors

No that we know the sector size of each staff on the circle, its time to represent the information on a pie chart.

chart source

(b) How much will be the salary of data entry officers if the total salary of workers is $144,000.

First we need to know the total number of workers there. They are 240 in number. There are 36 data entry officers. So to get their salary, we will divide the total salary by the number of workers and multiply by the figure for data entry officers.

Data entry officers salary = ($144,000/240) x 36
= 600 x 36
= $21,600

(c) What percentage of the workforce are security officers.

Percentage is over 100. So we get the figure for security officers and divide by the total. Then we can multiply by 100.

% workforce that are security officers= (30/240) x 100
= 0.125 x 100
= 12.5%

(d) What percentage of the salary is paid to drivers and office assistants?

We will solve the percentage salary for drivers and that of office assistants and add the two figures.

Drivers salary = ($144,000/240) x 44
= 600 x 44
= $26,400

To get the percentage, we divide 26,400 by 144,000 and multiply by 100
% for drivers = (26000/144000 x 100)
= 0.1833 x 100
= 18.33%

Office assistants salary = ($144,000/240) x 78
= 600 x 78
= $46,800

To get the percentage, we divide 46,800 by 144,000 and multiply by 100
% for drivers = (46800/144000 x 100)
= 0.325 x 100
= 32.5%

The total percentage of the salary paid to Drivers and Office assistants =
18.33 + 32.5
= 50.83%

Conclusion

You can clearly see that its easy to solve arithmetic problems involving pie charts. Just know how to calculate the sectors. From there, it is all too easy to solve for the unknow. We will see further examples in the next presentation.