One-variable data: distributions, center and spread

By the end you’ll be able to

Compute and compare mean, median, mode and range from lists, frequency tables, dot plots, histograms and box plots

Predict how adding or removing a value (including an outlier) changes the mean, median and standard deviation

Compare standard deviations of distributions qualitatively

Find a missing data value from a given mean or a change in mean

What the exam asks

Expect about one question per test on this skill, sometimes two, in either module. The common forms are:

Compute a statistic from a list, dot plot or frequency table (mean, median, mode, range).
Locate the median in a histogram or a large frequency table.
Read box plots: the five-number summary, and comparisons of two groups.
Use totals: find a missing value from a mean, the new mean after values are added or removed, or a combined mean of two groups (SPR is common here).
Predict effects: how an outlier, or a value added at the mean, changes the mean, median and standard deviation.
Compare spreads: which data set has the greater standard deviation, from dot plots, histograms or lists.

Statistic	How to find it	Sensitive to outliers?
Mean	sum ÷ number of values	Yes, strongly
Median	the middle value in order, or the average of the two middle values	Barely
Mode	the most frequent value	No

Median position: with $n$ values in order, the median is in position $\frac{n+1}{2}$ . If is even, average the values in positions and .

Change to the data	Mean	Median	SD and range
Add $c$ to every value	$+c$	$+c$	Unchanged
Multiply every value by $k > 0$	$\times k$	$\times k$	$\times k$
Remove a high outlier	Drops a lot	Drops a little or not at all	Decrease
Add a value equal to the mean	Unchanged	May shift slightly	SD decreases; range unchanged
Increase the maximum value	Increases	Unchanged	Increase