Mean, Median, Mode: 3 Different Measures of Central Tendency

Everyone needs help distinguishing between mean, median, mode and other statistical terms when first learning about averages. fotostorm / Getty Images

Mean, median, mode and sometimes range, are all different methods for finding probability distribution in statistics. Range can be a helpful yardstick when calculating data values that are close together, but it can quickly become confusing if there is a wide gap between the smallest value and the largest number.

Therefore, you will likely rely on mean, median, and mode when highlighting central tendency, or measures of center, in statistical data. The mean is the average, medians are the middle points, and mode highlights the most frequently occurring value.

What Are Data Points?

A data point, or data value, is an individual unit of information. Multiple data values are collected to create a data set. In statistical data analysis, this grouping allows someone to organize and compare all the values together before they draw conclusions that highlight important similarities and differences.

How to Calculate Mode

Mode is the most common number that occurs with the highest frequency among all the numbers in a data set. A typical mode is unimodal, meaning that the same number occurs more often than any other data value. However, you may find more than one mode in a large group of values.

For example, in the data set (1, 2, 2, 3, 4, 4, 5), there are two modes (2 and 4). This is commonly known as a bimodal mode, but any instance of multiple modes found in larger data sets can also be called multimodal.

How Do You Find Average Value?

There are two basic methods for calculating averages in data sets: arithmetic (sample) mean and geometric mean.

Geometric mean measures exponentials, such as calculating an interest rate formula for an investment, while the more commonly used arithmetic mean can help determine average income or population count.

The following is a step-by-step tutorial for calculating the arithmetic mean of the same data set from the previous paragraph.

Step 1: Add the Values to Find the Sum

1 + 2 + 2 + 3 + 4 + 4 + 5 = 21

Step 2: Divide the Sum by the Total Number of Values

Since there are 7 values in the data set, divide 21 by seven. The average value, or mean, is 3.

21 / 7 = 3

Is the Median Value the Same As the Middle Value?

Yes, except it is vital to organize your data set before selecting a middle number as an accurate median. For example, in the data set (1, 3, 2, 4, 5, 4, 2), the middle value is 4, but that's not necessarily the median.

To find the median, organize the group in ascending order (ending with the largest value) or descending order (beginning with the largest number); you'll get (1, 2, 2, 3, 4, 4, 5) and (5, 4, 4, 3, 2, 2, 1) respectively.

Since the data set contains an odd number of values, it is easy to find the middle number (3) in both examples. This is a much more accurate representation of the median value.

You can find the median of an even number of data points by calculating the mean of both middle values to find the middle point. For example, if the middle numbers are 3 and 4, you will add the two values together and divide them by 2:

3 + 4 = 7

7 / 2 = 3.5