Solving for the unknown in a Pie chart.

A pie chart is not just used to display statistical data, but it could be used to solve some unknown figures in a data set. In this presentation, I will demonstrate how one can solve for the unknown sectors of a pie chart.

You just need a basic knowledge of arithemetics in order to effective calculate the unknown. At the end of the day, you can even verify the accuracy of your answer since we all know that the inside angle size of a pie chart, which is equally a circle is 360^o. Lets work on one example.

Example 1: Consider the pie chart below. This is the distribution of different international languages spoken by students in a particular department.

Using the information provided by the Pie chart above, solve the following questions below:

1. Calculate the value of the figure labelled b.
2. Find the ratio of the students that speak English to that of those that speak German.
3.What percentage of the students speak Dutch?
4. What fraction of the students speak English?

Solution:

We will take the questions one after the other starting with the first question.

1. Calculate the value of the figure labelled b.

To solve this question, we will need to add up all the sectors and equate to 360 which is the size of the total angles of a circle.

105 + 75 + 3b + b + 2b = 360 (next add up and collect like terms)
6b + 180 = 360
6b = 360 - 180
6b = 180
b = 180/6
b = 30

Having found the value of the unknown, I can solve for the rest.

2. Find the ratio of the students that speak English to that of those that speak German.

The angle for English is 105. The angle for German is 2b = 2 x 30 = 60.
So the ratio of English to German is 105 : 60. Breaking it down, we have
35:20
7:4

3.What percentage of the students speak Dutch?
Angle for Dutch is 90.
So the percentage is 90/180 x 100 = 50%

4. What fraction of the students speak English?

The angle for English is 105. The total of all languages is 180.

Fraction for English is: 105/180 = 21/36

Conclusion

You can see that with this example, it is very easy to solve for the values of the unknown when you have a data presented in a Pie chart. Just follow the example above and you get it done.