This pie chart shows the results from a survey about people's favourite swimming strokes. a) What percentage of people said their favourite was butterfly stroke? b) 30% of people said their favourite was freestyle . How many degrees should the central angle of the freestyle sector be?

a) The number of people who said their favourite swimming stroke was butterfly stroke were not provided on the question asked. In order to find out the percentage, we would divide the number of individuals who indicated that their preferred stroke is butterfly by the total number of people, then multiply by 100, but since that information was not provide, we cannot directly answer this question.<br />The formula to this calculation would be \( \frac{\text{{no. of people that prefer butterfly stroke}}}{\text{{total no. of people surveyed}}})\times 100\% \)<br /><br />b) Freestyles representation is \( 30\% \) of the total, therefore it covers \( 30\% \) of the total in a pie chart. From basic mathematics we know that an angle of a sector of a circle (which is what pie charts are) is equivalent to the percentage that sector represents out of the total, which is 100%. Since the pie chart is displaying percentages out of a constantly constant, the entire pie represents \( 360^{\circ} \). <br /><br />Therefore, to find the angle of the Freestyle section of the pie chart we multiply \( 30 \% \) (so we convert it to 0.3) of \( 360^{\circ} \). That is, <br />\(0.3 \times 360^{\circ} \)<br />which gives \( 108^{\circ} \)<br />So, for question b) the central angle of the sector of the pie chart that represents freestyle should be \( 108^{\circ} \)