mean() — The average

The average — what everyone gets if you share it out evenly.

mean(x)

Key idea

• The mean is the average: add all values, then divide by how many there are. (e.g. mean of 2,4,6 = (2+4+6)/3 = 4)
• It acts as the balance point, where the data evenly tips on either side.
• A single outlier (a far-off extreme value) can pull the mean far from the typical case. (e.g. mean of 2,4,90 = 32)
• Comparing the mean with the median (the middle value) helps you spot skew in the data.
• If the mean is much higher than the median, the data is skewed right (a long tail of large values). (e.g. mean 32 vs median 4)

Definition

$$\bar{x}=\frac{1}{n}\sum _{i=1}^n{x}_i$$

$x_i$

each value

$n$

how many values

$\bar{x}$

the result — the average (balance point)

$\sum$

add them all up

$$\bar{x}=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6$$

Where you'd use it

• Five friends are 150, 160, 170, 180, 190 cm tall. mean adds them to 850 and divides by 5 to give 170 cm, the average height of the group.
• A player scores 10, 20, 12, 18 points across four games. Their average is mean = 60 ÷ 4 = 15 points per game, a single figure summing up their form.
• Milk costs $1.80, $2.00, $2.20 at three nearby shops. The mean price is $2.00, a quick sense of what you would typically pay.

Frequently asked questions

Why is my mean NA?

A missing value makes it NA. Use mean(x, na.rm = TRUE) to ignore them.

Mean or median?

For skewed data or outliers, the median is usually more representative.