To determine the variance of a sample we can use the following formula:
[tex]s^2=\frac{\sum(x_i-\bar{x})}{n-1},[/tex]
where
[tex]\bar{x}\text{ }[/tex]
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:
[tex]\bar{x\text{ }}=\frac{50.0+51.5+53.0+53.5+54.0}{5}=52.4.[/tex]
Substituting the above result in the formula for the variance, we get:
[tex]s^2=2.675.[/tex]
Therefore, the standard deviation is:
[tex]s=1.6355427.[/tex]
Answer:
Variance:
[tex]s^2=2.675.[/tex]
Standard deviation:
[tex]s=1.6355427.[/tex]
