summary() — Five-number summary

summary(x)

Key idea

• summary gives a quick overview: the smallest, largest, middle, and average of your numbers, plus the quartile cut-off points.
• It reports the minimum (smallest) and maximum (largest) to show the overall range. (e.g. min and max)
• It includes Q1 (bottom-quarter cut-off), the median (middle), and Q3 (top-quarter cut-off) to show the spread. (e.g. Q1, median, Q3)
• Showing the mean (average) next to the median helps reveal skew (a lean to one side). (e.g. mean vs median)
• It is a fast way to understand a dataset before plotting it.

Definition

$$\{\min ,Q_1,\text{median},Q_3,\max \}$$

$\min ,\max$

smallest and largest values

$Q_1,Q_3$

lower and upper quartiles

$\text{median}$

the middle value

Where you'd use it

• You just received a column of 200 test scores. Running summary reports the minimum, quartiles, median, mean, and maximum in one line — say min 41, median 74, max 99 — so you grasp the whole batch before drawing any chart.
• For a list of house prices, summary shows the cheapest, the typical (median) price, and the priciest at once; if the mean comes out well above the median, you immediately suspect a few expensive homes are skewing things.
• Before charting 300 delivery times, a quick summary tells you they run from about 10 to 90 minutes with a median near 25, sizing up the spread in a single glance.

Frequently asked questions

Does summary() include the SD?

No — it gives min, quartiles, median, mean and max. Call sd() separately.