P12 | Maths Made Easy

P12

QUESTION: 80 people are asked to throw a ball as far as they can, and the results are recorded. Using the data in the table below, find an estimate for the mean throwing distance in this experiment.

 

ANSWER: Firstly, we need to find the midpoints of each class and write them in a new column attached to the one given in the question.

Then, treat the midpoints as the actual values and find the sum of all the midpoints. To make this quicker, we multiply each midpoint by its frequency, and sum all the results. Then, since we are estimating the mean, we divide by the total number of people in the experiment: 80. Doing this, we get

\text{estimated mean }=\dfrac{(21\times10)+(43\times30)+(12\times55)+(4\times90)}{80}= \dfrac{2,520}{80}=31.5