# Means and medians

Andy Wills

### Median

data

[1]  1  2  2  3  3  3  4  4 50

• The median is the middle number when the data is put in order
median(data)

[1] 3


### Mean

data

[1]  1  2  2  3  3  3  4  4 50

• The mean is the sum of all the numbers (72), divided by the sample size (9), giving:
mean(data)

[1] 8


### Comparison

data

[1]  1  2  2  3  3  3  4  4 50

• In this case, the mean (8) is bigger than nearly all the numbers. This means it's not very representative of its sample.

• The mean will always be unrepresentative when there are a few numbers that are very high (or very low), compared to the rest.

• In these cases, we sau the distibution is skewed.

### Skewness

• Our income data is skewed, so the median gives a better indication of average salary than the mean in this case.