Question

Calculate the variance and standard deviation ofthe samples, using the appropriate symbols to label each

Answer 1

To determine the variance of a sample we can use the following formula:

`s^2=\frac{\sum(x_i-\bar{x})}{n-1},`

where

`\bar{x}\text{ }`

is the mean of the dataset.

The standard deviation is the square root of the variance.

Recall that the mean of a dataset is the sum of the number divided by the number of numbers, therefore, the mean of the given dataset is:

`\bar{x\text{ }}=(50.0+51.5+53.0+53.5+54.0)/(5)=52.4.`

Substituting the above result in the formula for the variance, we get:

`s^2=2.675.`

Therefore, the standard deviation is:

`s=1.6355427.`

Answer:

Variance:

`s^2=2.675.`

Standard deviation:

`s=1.6355427.`