IB Mathematics Applications & Interpretation Question Type 7: Determining the Effect on Mean, Mode, Median, Range, Variance, Standard Deviation and IQR Given Specific Transformations of Data Exercises

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

If a new data point $10$ is added to the set $S=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$, calculate the new mean.

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

Compute the sum of all values in the data set $X=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

How many values in $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ exceed the mean of the set?

Compute the population variance of the following dataset: $$\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$$ Use the formula ${\sigma }^2=\frac{1}{N}\sum x_i^2-{\bar{x}}^2$.

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

Determine the lower and upper quartiles ($Q_1$ and $Q_3$) of the data set $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

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

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

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