# Statistics: Mean, Median, and Mode

## Introduction

Mean, median, and mode are often calculated to describe a dataset as they are useful measures of central tendency.

The mean, or arithmetic average, is the sum of all numbers in a set divided by the amount of numbers. For example, given the set [2, 3, 4], the mean is 3, or (2+3+4)/3. The mean is important because it tells you what the average number amongst a group is. This is a vital thing to know when working with statistical data as many other operations are based on knowing the mean.

The median is the middle number within the set, therefore 3 is the median in the above example as well. The mean and the median do not, and often are not the same number however. For instance in the set [2, 3, 100], 3 is still the median but the mean is 35, or (2 + 3 + 100)/3. The median is important because it shows you what the middle number is amongst a group. Unlike the mean which adds all numbers together and thus hides outliers, the median shows the true center of a group.

Finally, the mode is the most commonly occurring number. In the set [2, 2, 3, 4], the mode is 2. Excel has formulas to help find each of these values from a selected numberset, making them very easy to determine. The mode tells you what the most common number is.

## Functions

Utilizing the given Harry Potter-based data, your professor asks you to find the mean, median and mode of the House Points (Column Q). To calculate the mean of the data set select an empty cell and type =AVERAGE(Q2:Q26). You can also select the cells with your cursor rather than typing the desired cell.

After calculating the mean, select another empty cell and type =MEDIAN(Q2:Q26).

After calculating the median, select another empty cell and type =MODE(Q2:Q26). Check your calculations with the numbers below.

Mean: 4

Median: 15

Mode: -97

As the data above suggests, it is important to use the appropriate method of central tendency in order to describe the data accurately.

Mean

**=AVERAGE(****range****)**

Median

**=MEDIAN(range)**

Mode

**=MODE(range)**

## Practice

Practice finding the mean, median, and mode of data by answering the question in the highlighted cell.

- What is the global mean, median and mode of CO2 emissions in metric tons (Column G)?

## Answer:

Mean: 175806.2827, Median: 11590, Mode: 180,

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## Conclusion

Mean, median and mode are three descriptive statistics that let you know more about the data you are working with. It is always good to find out these three metrics as well as the maximum and minimum when you start working with data before moving on to other statistical analysis. Although all three appear to show similar things, the information you get from each are very different and important to compare.