Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.

Tablet Computers. Tablet personal computers such as iPad and Kindle Fire are one piece portable computers that typically offer a touchscreen. Tablets are available in different sizes but generally offer a screen that is greater than $7$inches diagonally. Consumer Reports reviews tablets of different sizes and Internet capabilities. The battery lives, in hours, for a sample of tablets with screen sizes between $9$and $12$inches are provided in the following table.

role="math" localid="1651995977208" $8.4,5.6,10.9,10.8,11.5,8,8.5,12.9$

Step by step solution

01

Step 1. Given information.  

We have given data:$8.4,5.6,10.9,10.8,11.5,8,8.5,12.9$

02

Step 2. To find range of the data.  

$$\begin{gathered} Range=Max.value-Min.Value \\ =12.9-5.6 \\ =7.3 \end{gathered}$$

03

Step 3. To find mean of the data.

$$\begin{gathered} Mean=\frac{Sumofobservation}{Numberofobservation} \\ =\frac{8.4+5.6+10.9+10.8+11.5+8+8.5+12.9}{8} \\ =\frac{76.6}{8} \\ =9.58 \end{gathered}$$

04

Step 4. To find standard deviation of the data. 

$x$	$x-\overline{x}$	${\left(x-\overline{x}\right)}^2$
$$\begin{gathered} 8.4 \\ 5.6 \\ 10.9 \\ 10.8 \\ 11.5 \\ 8 \\ 8.5 \\ 12.9 \end{gathered}$$	$$\begin{gathered} -1.18 \\ -3.98 \\ 1.32 \\ 1.22 \\ 1.92 \\ -1.58 \\ -1.08 \\ 3.32 \end{gathered}$$	$$\begin{gathered} 1.39 \\ 15.84 \\ 1.74 \\ 1.49 \\ 3.69 \\ 2.50 \\ 1.17 \\ 11.02 \end{gathered}$$

localid="1652001425844" $$\begin{gathered} S\tan darddeviation=\sqrt{\frac{{\displaystyle \sum _{}}{\left(x-\overline{x}\right)}^2}{n-1}} \\ =\sqrt{\frac{38.84}{8-1}} \\ =\sqrt{\frac{38.84}{7}} \\ =\sqrt{5.5485} \\ =2.36 \end{gathered}$$

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