Data Analysis: Mean, Median, Mode, and Range

Learning Objectives

Define the four main measures used to describe a set of data: mean, median, mode, and range.

Calculate the mean, median, mode, and range for a given data set.

Explain what each measure tells you about the data.

Identify which measure of center is most affected by an outlier.

Making Sense of Numbers

When you have a set of data, like the test scores for a class or the heights of a group of people, how can you describe the data in a simple way? We use a few key values to summarize the data. These values tell us about the 'center' of the data and how 'spread out' it is.

Measures of Central Tendency

These are numbers that describe the 'middle' or 'typical' value of a data set.

1. Mean (The Average)

The mean is what most people call the 'average'. It is the most common measure of center.

How to find it: Add up all the values in the data set, and then divide by the number of values.

Example Data Set: {2, 2, 3, 5, 8}

Calculation: (2 + 2 + 3 + 5 + 8) / 5 = 20 / 5 = 4

Mean = 4

2. Median (The Middle)

The median is the middle number in a data set that has been arranged in order from least to greatest.

How to find it: First, put all the numbers in order.

If there is an odd number of values, the median is the number right in the middle.

If there is an even number of values, the median is the average of the two middle numbers.

Example Data Set: {8, 2, 5, 2, 3}

Step 1: Order the data: {2, 2, 3, 5, 8}

Step 2: Find the middle: The middle number is 3.

Median = 3

3. Mode (The Most Often)

The mode is the value that appears most frequently in a data set.

How to find it: Look for the number that shows up more than any other number.

Example Data Set: {2, 2, 3, 5, 8}

Calculation: The number 2 appears twice, more than any other number.

Mode = 2

A data set can have more than one mode, or it can have no mode if every value appears only once.

Measure of Spread

This value tells you how spread out the data is.

4. Range (The Spread)

The range is the difference between the highest value and the lowest value in a data set.

How to find it: Subtract the smallest value from the largest value.

Example Data Set: {2, 2, 3, 5, 8}

Calculation: Highest value (8) - Lowest value (2) = 6

Range = 6

The Effect of Outliers

An outlier is a value in a data set that is much larger or much smaller than the other values. Outliers can have a big effect on some of our measures.

The mean is very sensitive to outliers. A single very high or very low value can pull the mean up or down significantly.

The median is not affected by outliers. Since it's just the middle number, an extreme value at either end won't change its position.

For this reason, the median is often a better measure of the 'typical' value when a data set has strong outliers.

Key Terms

**Mean: The average of a set of numbers, found by adding all the values and dividing by the number of values.
**Median: The middle value in a data set when the numbers are listed in order from least to greatest.
**Mode: The value that occurs most frequently in a data set.
**Range: The difference between the largest and smallest values in a data set.
**Outlier: A data point that is significantly different from other data points in a set.

Data Analysis: Mean, Median, Mode, and Range

Learning Objectives

Making Sense of Numbers

Measures of Central Tendency

Measure of Spread

The Effect of Outliers

Key Terms

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