Question

A distribution of data has a maximum value of 96, a median value of 59.5, and a minimum of 23.

Answer 1

Given:

Maximum value = 96

Minimum value = 59.5

Median value = 59.5

Let's use the range rule of thumb to estimate the standard deviation.

The range rule of thumb states that the range is four times the standard deviation.

Thus, we have the formula:

`\begin{gathered} range=sd*4 \\ \\ sd=(range)/(4) \end{gathered}`

Where:

Range = Maximum value - Minimum value

To estimate the standard deviation using the range rule of thumb, we have:

`\begin{gathered} sd=(range)/(4)=(max-min)/(4) \\ \\ sd=(96-23)/(4) \\ \\ sd=(73)/(4) \\ \\ sd=18.25\approx18.3 \\ \end{gathered}`

Therefore, the standard deviation is approximately 18.3

ANSWER:

18.3