Question

Standard deviations (6.1) Continuous random variables A, B, and C all take values between 0 and 10 . Their density curves, drawn on the same horizontal scales, are shown here. Rank the standard deviations of the three random variables from smallest to largest. Justify your answer.

Short answer

the standard deviations from smallest to largest is B, C, A.

Step-by-step solution

Given Information

The figures are

Simplification

The standard deviation calculates the average departure of the data values from the mean.$\mu$.

This then means that if more number of data values lie closest to $\mu$, then the standard deviation would be smaller.

Because the peak of the density curve is largest at, the standard deviation of B is the least. $\mu$and therefore the most of the data values lie very close to the means $\mu$.

The standard deviation of A is largest, because of the peak of the density curve is the highest at the points furthest from the mean $\mu$and therefore the most of the data values lie far away from the mean $\mu$.

As a result, the standard deviations from lowest to greatest are $B,C,A$.