Before a single number gets calculated, a histogram should be named. Is there one hump or two? Does one side run further than the other? Is there any hump at all? Every histogram below is counted from values simulated on the spot, and the mean, median and skewness are computed from those same values — so you can drag a shape into existence and watch the numbers follow it.
The histogram
The five shapes
Five simulated samples of 400 values each, drawn from five different populations. Tap one to load it above. Notice that symmetric, uniform and an even bimodal are all balanced left-to-right — balance alone does not finish the sentence.
Name the shapepick a shape, or switch to the quiz
6.5 cm
300
Values n300
Mean—
Median—
Mean − median—
Apparent peaks—
SD—
Sample skew g₁—
Population skew—
Which shape is this?
Asked0
Correct0
Streak0
Best streak0
Skew is named for the tail, not the hump. The tail is the thin side that keeps going; the hump is the fat side where most of the data sit. Point at the thin side and you have said the name — tail trailing off to the right is skewed right, even though the hump is on the left. Nearly every mistake in this section is a student naming the hump.
The mean–median check is a rule of thumb, not a theorem. For the single-humped continuous variables you meet in this course, a right tail comes with mean > median and a left tail with mean < median, because the mean is the balance point and a long tail drags it while the median barely moves. But counter-examples are real, and lumpy, discrete or multi-peaked data sets are the usual offenders: distributions exist whose tail runs one way while the mean sits on the other side of the median. Read the picture first. Use the numbers to confirm what you saw, never to overrule it.