Q 3.4. - The Practice of Statistics for AP

Question

The heights (in inches) of the five starters on a basketball team are $67, 72, 76, 76, \mathrm{and} 84.$

Interpret the meaning of the standard deviation in the given setting.

Step-by-Step Solution

Answer

The interpretation of standard deviation shows the difference between the height of starters and the average height of players in the team and the difference is $\mathbf{6}\mathbf{.}\mathbf{245}$. 

Step 1: Given information

Given data : 

The heights five starters are : $67, 72, 76, 76, \mathrm{and} 84.$

Step 2: Concept

The formula to derive the Standard deviation is: $$\begin{gathered} s =\sqrt{\frac{\Sigma {(x-\overline{x})}^2 }{n-1}} \\ \overline{x} = \frac{\Sigma x }{n} \end{gathered}$$

Step 3: Calculation

The formula to compute the standard deviation is:

$$\begin{gathered} s =\sqrt{\frac{\Sigma {(x-\overline{x})}^2 }{n-1}} \\ \overline{x} = \frac{ \Sigma x }{n} \end{gathered}$$

The standard deviation is calculated using a Ti-83 calculator as follows: 

Thus, the standard deviation is $6.245$ The standard deviation indicates that the difference in height between the starters and the average player is roughly $6.245$