Center of a Distribution vs Spread of a Distribution
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Center of a distribution
Describing data
The center of a distribution is its typical value, reported with the mean when the shape is roughly symmetric and with the median when it is skewed.
Center is one of the features a full description of a quantitative distribution covers, alongside shape, variability, and unusual features such as outliers, gaps, or clusters. The two standard measures are the mean (x-bar) and the median, and shape decides which one you quote, since the mean follows a long tail while the median mostly ignores it. Take the values 3, 5, 6, 8, 28: the mean is , the median is 6, and 6 is the better summary of where a typical value sits. Pair the mean with the standard deviation and the median with the IQR so your center and spread match.
Spread of a distribution
Describing data
The spread of a distribution is how far apart its values are, summarized by the range, the interquartile range, or the standard deviation.
Spread is the width of the data, and the measure you report has to match the measure of center you reported with it. Pair the mean with the standard deviation, and pair the median with the IQR, which uses the median-excluded (TI-84) quartile rule on this site; the range is the crudest option because it depends only on the two extremes. For the values 10, 12, 14, 16, 18 the mean is 14, the range is , and the sample standard deviation is . Two data sets can share the same center and still look nothing alike once you compare their spread.