In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class and a mean of 1.39 litres, what is the estimated standard deviation of the amount of water taken, correct to 3 decimal places?

Model answer

0.613

Also accepted: 0.61

Explanation

\sum fx^2 = 230.75

, so variance

= \frac{230.75}{100} - 1.39^2 = 2.3075 - 1.9321 = 0.3754

, giving SD

= \sqrt{0.3754} \approx 0.613

litres.

Derived from ZIMSEC Statistics Paper 2, November 2019, Q2

More questions from this paper

Danho has every sitting for this paper, with your progress tracked question by question, offline.