Pick mean, median, or mode by the shape of the data, predict which one an outlier drags and which one holds, and read the mean-median gap as a numerical measure of skew.

Six salaries, `[52, 55, 58, 60, 64, 240]`, and two honest people report the typical pay as $88k and $59k. Both did the arithmetic right; the number you trust depends on which question you asked.

Square each value's gap from the mean into the variance, square-root it back to a standard deviation in the data's own units, then rescale any value to a mean-zero, standard-deviation-one z-score for feature preprocessing.

Two classes both average 75 on one test, `[73, 74, 75, 76, 77]` and `[55, 65, 75, 85, 95]`. By that average they look identical, yet one class is ten times more spread out than the other.

Pin a bell curve down with just two numbers, a center and a width, apply the 68-95-99.7 rule to turn any standard-deviation band into a percentage of the data, and read a value's percentile by standardizing it onto the single standard normal, then catch where skewed data breaks the rule.

Line up the heights of a thousand adult men and they pile into a smooth hump: most crowd near `69` inches, thinning fast toward the very tall and the very short. Two numbers describe that whole pile.

Tally the successes in `n` independent yes/no trials at a constant rate `p`, read the center `np` and spread `√(np(1-p))` straight from those two numbers, and swap in the normal approximation once `np` and `n(1-p)` both clear `10`.

Blast a signup offer to 200 inboxes, each person clicking or ignoring at the same 3% rate. You will rarely get exactly 6 clicks twice: the count wanders, and its entire spread rides on just two numbers.

Average two columns' standardized products into a single number in `[−1, +1]`, test it against Anscombe's quartet to see what one summary hides, then separate cause from reverse cause, a confounder, and coincidence by assigning the treatment at random.

A spreadsheet column of hours slept and a column of exam scores drift up together, and `corr()` hands you one number for the whole pattern, but that number stays silent about which one moved the other.

Pair two columns' deviations into a covariance, stack every pair into one symmetric matrix built in one line as centered data times its own transpose over n − 1, then read the diagonal as each column's spread and the off-diagonal as the cloud's tilt, and divide out the units for the correlation matrix.

Line up two columns of a health survey, height and weight; variance scores them one at a time, but pair their gaps and a single `np.cov(data)` call folds the whole spreadsheet's spread and tilt into one grid of numbers.