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# Mean, median and mode

Mean, median and mode are used to find central tendencies in a dataset.

## Mean

The mean is what we usually call the average and is therefore the sum of the data divided by the number of data points.

## Median

The median is the middle number of a dataset. Say we have the three numbers:

1, 2, 3.

Here, 2 is the middle number and thus the median.

In case we have even number of datapoints like: 1, 3, 9, 15, we take the average of the two middle datapoints which in this case are 3 and 9, so our median in this case (3+9)/(2) = 6.

The median can be more appropriate than the mean. It can give a more realistic picture of a given situation.

## Median example

An example is where the general economical wealth is said to improve over a certain period, whereas the mean income has increased. But what has really happened is that the rich have become much richer and the pool of poor also has increased and has become even more poor. In this case, the median gives a more realistic picture.

Say that the population consists of 4 persons with low incomes of 5; 7; 11 and 12 euros per month and one rich person with an income of € 1,000. The mean income of the population is € 174. A very un-realistic description of the true population. Using the median (7+11/2 = 9) the rich person’s income is observed as an outlier.

In that way, median can give a more realistic picture of a dataset with outliers. However, there are disciplines that help handling outliers and typically the mean is used rather than the median.

## Mode

The mode is the most frequently occurring number in a dataset. In the dataset 1, 2, 4, 4, 4, 10, 12 the mode is 4. In case there is no mostly common occurring number, then there is no mode.

## Mean, median and mode visualized In Interquartile range (IQR) and boxplots I look further into mean, median and mode.

## With MS Excel

Excel functions that work with these concepts are

=AVERAGE()

=MEDIAN()

=MODE.MULTI() ## Learning resources

Khan Academy video: Statistics Intro: Mean, median & mode #### Carsten Grube

Freelance Data Analyst

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