# 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

##### Two-sample inference

##### Normal distribution

##### Confidence intervals

##### Simple linear regression, fundamentals

##### ANOVA & the F-distribution

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