Z-score calc

What is the Z Score for the following numbers:

X is 16, and data for the population mean, and the standard deviation is 196, 193, 79, 30, 29, 81, 25, 21, 164

Level of difficulty = 2 of 2
Please format it to 2 decimal places.

Correct answer:

z =  -1.01

Step-by-step explanation:

$$\begin{gathered} X=16 \\ s=196+193+79+30+29+81+25+21+164=818 \\ n=9 \\ \mu =s/n=818/9=\frac{818}{9}=90\frac{8}{9}\doteq 90.8889 \\ r=(196-\mu {)}^2+(193-\mu {)}^2+(79-\mu {)}^2+(30-\mu {)}^2+(29-\mu {)}^2+(81-\mu {)}^2+(25-\mu {)}^2+(21-\mu {)}^2+(164-\mu {)}^2=(196-90.8889{)}^2+(193-90.8889{)}^2+(79-90.8889{)}^2+(30-90.8889{)}^2+(29-90.8889{)}^2+(81-90.8889{)}^2+(25-90.8889{)}^2+(21-90.8889{)}^2+(164-90.8889{)}^2=\frac{394406}{9}=43822\frac{8}{9}\doteq 43822.8889 \\ \sigma =\sqrt{r/(n-1)}=\sqrt{43822.8889/(9-1)}\doteq 74.0126 \\ z=\frac{X-\mu }{\sigma }=\frac{16-90.8889}{74.0126}=-1.01 \end{gathered}$$

Try another example