Mean

The mean is the average value in the dataset.

It is calculated by adding up the data values (x), then dividing by the number of items (n).

The mean of a sample is traditionally labelled x-bar. The mean of a population is labelled µ (mu).

sum(x)/n = x-bar

For example, find the mean of the following sample dataset:

10
12
1
16
10
11
13
6
15
6

sum(x) = 10+12+1+16+10+11+13+6+15+6 =100

n=10

x-bar = 100/10 = 10

The mean is 10.

It is also the "center" of the data - in the sense that the difference of each value from the mean will sum up to zero. This is because there are equal positive differences as there are negative.

Check this, using the above example:

10 - 10 = 0
12 - 10 = 2
1 - 10 = -9
16 - 10 = 6
10 - 10 = 0
11 - 10 = 1
13 - 10 = 3
6 - 10 = -4
15 - 10 = 5
6 - 10 = -4

0 + 2 + -9 + 6 + 0 + 1 + 3 + -4 + 5 + -4 = 0

The mean, median, and mode are all measures of central tendency. The skew can be determined by comparing these three measures.

Mode

Mode is the value in a dataset that appears the most frequently.

For example:

In the following the sample, the mode is 5

1
1
2
5
6
2
9
5
7
5
2
5
9
5

Count the number of times 5 appears. It appears the most, so it is the mode.

Some datasets have more than one mode.

If there is a single mode, the term 'unimodal' is used. The example above is unimodal. There are five 5's. Had there also been five 2's, than the example is no longer unimodal. Then, both five and two would be called modes.

The mean, median, and mode are all measures of central tendency. The skew can be determined by comparing these three measures.