IB Mathematics Applications & Interpretation 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 $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.