Question

Stephen Gould of Harvard University noted that the mean batting average has been steady but standard deviation has been decreasing. what does standard deviation have to do with batters not being able to reach 0.400 batting averages?

Answer 1

It is given that the mean batting average has been steady but standard deviation has been decreasing.

Now we know coefficient of variation(CV) =SD/mean

Where SD= standard deviation of batting average.

As CV is a useful statistic for comparing the degree of variation from one data series to another. If CV increases, variance increases, consistency decreases.

Here, even if the mean is not changing, the numerator i.e the sd is decreasing hence the CV is decreasing so consistency is increasing. i.e the batsmen are maintaining the same performance as they were giving previously. So if the batters were not being able to reach 0.400 batting averages previously, as standard deviation is decreasing, they are maintaining there previous performance as indicated by the CV hence not being able to achieve 0.4 batting average.