Question Type 7: Determining the effect on mean, mode, median, range, variance, standard deviation and IQR given specific transformations of data Bootcamps

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

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 $x_i'=x_i+4$, determine how the following summary statistics change: mean, median, mode, range, variance, standard deviation, and IQR.

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

Given the same dataset $x_1,\dots,x_n$, each value is multiplied by 3 to form $x_i'=3x_i$. State how mean, median, mode, range, variance, standard deviation, and IQR change.

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

A dataset $x_1,\dots,x_n$ is transformed by $x_i''=x_i-\bar x$ (mean-centering). Determine the new mean, median, mode, range, variance, standard deviation, and IQR.

A dataset has minimum $m$ and maximum $M$. You increase the maximum to $M+1$ and decrease the minimum to $m-1$. How do mean, median, mode, range, variance, standard deviation, and IQR change?

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.

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

If the largest value of a dataset is increased by 5 (all other values unchanged), what is the qualitative effect on mean, median, mode, range, variance, standard deviation, and IQR?

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?

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.