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

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 $1.5 \times \text{IQR}$ 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.

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

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

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

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

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

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