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

If the smallest value of a dataset is decreased by 3 (others unchanged), describe the effect on mean, median, mode, range, variance, standard deviation, and IQR.

A dataset has a minimum value $m$ and a maximum value $M$. The maximum value is increased to $M+1$ and the minimum value is decreased to $m-1$.

State how the mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) change.

Transform each value by $x_i^{\prime }=5x_i+10$. Describe the effect on the mean, median, mode, range, variance, standard deviation and IQR.

A dataset has minimum $m$ and maximum $M$. You replace $M$ by $2M$ and $m$ by $m/2$, leaving other values unchanged. Describe the changes to mean, median, mode, range, variance, standard deviation, and IQR.

Consider a dataset $x_1,\dots ,x_n$. Each value is multiplied by 3 to form a new dataset where $x_i^{\prime }=3x_i$.

State how the mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) change.

Suppose you multiply every data value by $-2$. How do mean, median, mode, range, variance, standard deviation, and IQR change?

If you add 7 to the maximum value and subtract 7 from the minimum value of a dataset (others unchanged), how are mean, median, mode, range, variance, standard deviation, and IQR affected?

If every data point is divided by 4, state the changes to mean, median, mode, range, variance, standard deviation, and IQR.

Transform a dataset to z-scores via $z_i=\frac{x_i-\bar{x}}{s}$, where $s$ is the original standard deviation. Explain the effect on mean, median, mode, range, variance, standard deviation, and IQR.

Suppose a dataset consists of values $x_1,x_2,\dots ,x_n$. If every value is increased by 4 to form a new dataset $x_i^{\prime }=x_i+4$, determine how the following summary statistics change: mean, median, mode, range, variance, standard deviation, and IQR.

The dataset is transformed by $y_i=x_i-\bar{x}$ (mean-centering). Determine the new mean, median, mode, range, variance, standard deviation, and interquartile range (IQR) in terms of the original statistics.