Question

I only need the correct answer. This is part one 1 out of 3.

Answer 1

Part 1

To find the range, we subtract the lowest value from the greatest value, ignoring the others.

So, in this case, we have:

• Lowest value: 20.3

,

• Greatest value: 110.4

`\text{Range = }110.4-20.3=90.1`

Therefore, the range is 90.1

Part 2

The formula to find the variance is

`\begin{gathered} \sigma^2=\frac{\sum ^{}_{}(x-\mu)^2}{n} \\ \text{ Where} \\ x=\text{ data values} \\ \mu=\text{ mean} \\ n=\text{ number of data points} \end{gathered}`

The formula to find the mean is

`\mu=\frac{\sum ^{}_{}x}{n}`

So, as you can see, we first find the mean, and with this value, we find the variance of the data set.

• Mean

`\begin{gathered} \mu=(20.3+33.5+21.8+58.2+23.2+110.4+30.9+24.4+74.6+60.4+40.8)/(11) \\ \mu=(498.5)/(11) \\ \mu=45.32 \end{gathered}`

• Variance

Therefore, the variance is 723.66.