How to represent the following data in a pie chart.

Question

In the following diagram are reported the sports practiced by alumns of a school. $$ \begin{array}{c|lcr} \text{Sport} & \text{Alumns($n^\circ$)} \\ \hline \text{Soccer} &15 \\ \text{Basketball} & 12 \\ \text{volleyball} & 6 \\ \text{Tennis} & 3 \\ \end{array} $$ Represent with a pie chart the distribution of the various sports between alumns.

My effort

My main difficulty is translating the numbers given in the above diagram into percentages so that I know what fraction of a circle they do represent.

Defining $x$ to be the total number of the alumns I have that $\cfrac{15}{x}$ is the percentage of them practing soccer and the rest follows.

My thought is that I can find $x$ by solving $\cfrac{15}{x}+ \cfrac{12}{x}+\cfrac{6}{x}+\cfrac{3}{x}=1$ since the percentages must add to $1$ and this would yield the solution $x=36$.

So the percentage of alumns practing soccer would be $\cfrac{15}{36}\approx 40 \% $,practicing basket $\approx 30 \%$,practing volleyball $\approx 16\%$ and finally the percentage of those practing tennis would be $\approx 8 \% $

So if we let $S,B,V,T$ be the letters representing the respective sport I would have

The above diagram was really made by heart rather than precise methods(the pie chart is from the problem,so the twelve points on the circumference are equally spaced) .

Question Is my reasoning okay ?What is a precise manner to solve these kind of exercises ?

Answer 1

Your calculation of percentages is approximately correct, but you're doing too much work trying to solve for $x$ in your equation. Note that $x$ is exactly equal to the total number of alumni you have: $x = 15 + 12 + 6 + 3 = 36$.

So, in general, let's say you want to find the proportion of people who play soccer. 15 out of the 36 people play soccer, so the proportion as a fraction is $\frac{15}{36} = 0.4166...$

If we want to convert this to a percentage we multiply by 100 to arrive at $41.66\%$.

And finally, what we really want is how many degrees of a full circle it will take up. Instead of multiplying by 100 like we did for the percentage, we'll multiply by 360. $\frac{15}{36}*360 = 150^\circ$.

Your circle is divided into 12 equal parts, so each part is $\frac{360^\circ}{12} = 30^\circ$.

So, the number of parts the soccer members will take is $\frac{150^\circ}{30^\circ} = 5$ parts, which is consistent with what you've shown on the diagram. (:

Answer 2

You are correct and your reasoning is valid. However, your math on getting the percentage is not quite correct (for example $15/36=0.41666666$ which can be rounded to say $0.42$ or $0.417$ but you have to be consistent with the number of digits to round to across all pairs of values). Excel plots your data as below: