EasyMathematicsHigh School (11–12)Statistics and ProbabilityNumerical

A coach times two runners over many laps of a track…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A coach times two runners over many laps of a track. Runner A has a mean lap time of $60$ seconds with a standard deviation of $3$ seconds. Runner B has a mean lap time of $90$ seconds with a standard deviation of $4$ seconds. The coach wants to know which runner is steadier relative to the usual lap time. Find the coefficient of variation for each runner, and say which one is more consistent.

Need a reminder? The key ideaShow

$\text{CV} = \dfrac{\sigma}{\bar{x}} \times 100\%$ , and the smaller CV is the more consistent. For $y = a x + b$ : $\bar{y} = a\bar{x} + b$ and $\sigma_y = \lvert a \rvert\,\sigma_x$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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