Question

U.S Supreme Court Justices. From Wikipedia, we found that the ages of the justices of the U.S Supreme Court, as of September 9, 2013, are as follows, in year.

Part (a) find $n$

Part (b) Compute$\sum _{}{x}_i$

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

Short answer

Part (a) 9

Part (b) 607

Part (c) 67.4

Step-by-step solution

Part (a) Step 1. Given information.

The provided data set is:

58, 77, 77, 65, 80, 75, 63, 59, 53

Part (a) Step 2. The value of n 

The given collection is: 58, 77, 77, 65, 80, 75, 63, 59, 53

The number of samples is 9

Then

$n=9$

As a result, the value of n is 9.

Part (b) Step 1. Given information.

The provided data set is:

58, 77, 77, 65, 80, 75, 63, 59, 53

Part (b) Step 2. The value of ∑xi

The value of $\sum _{}{x}_i$is calculated as follows:

$$\begin{gathered} \sum _{}{x}_i=58+77+77+65+80+75+63+59+53 \\ \sum _{}{x}_i=607 \end{gathered}$$

As a result, the value of $\sum _{}{x}_i$is 607

Part (c) Step 1. Given information.

The provided data set is:

58, 77, 77, 65, 80, 75, 63, 59, 53

Part (c) Step 2 The sample average.

Mean is expressed as follows:

$\overline{x}=\frac{\sum _{}x}{n}$

The mean of the given data set is computed as follows:

$$\begin{gathered} \overline{x}=\frac{607}{9} \\ \overline{x}=67.4 \end{gathered}$$

As a result, the sample mean days is 67.4.