Question Type 5: Given a data set, finding the value of the standard deviation, variance and IQR Exercises

Compute the range of the data set $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Find the population standard deviation of the data set $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Find the interquartile range (IQR) of the data set $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Determine the sample standard deviation of $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Calculate the sample variance of the data set $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Calculate the population variance of the data set $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

If each value in $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ is multiplied by 2, find the new population variance and standard deviation.

If each value in $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ is increased by 5, what are the new population variance and standard deviation?

What proportion of observations in $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ lie within one population standard deviation of the mean?

Identify any outliers in $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ using the $1.5\times\mathrm{IQR}$ rule.

A new observation $40$ is added to the original data set $\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$. Determine the new population variance.