Mean, Median, Mode, & Range Definitions & Examples

In statistics, there are four main measures of central tendency: mean, median, mode, and range. These measures are used to describe the data set by finding the center of the data. The mean is the most common measure of central tendency and it is simply the average of all the data points. The median is the middle value of the data set and mode is the most frequently occurring value. The range is the difference between the highest and lowest values in the data set. We will explore each of these measures of central tendency in more depth and provide examples to help you better understand them.

What is Mean, Median, and Mode?

The mean, median, and mode are all ways of measuring central tendency in a data set. The mean is the average of all the values in the data set, the median is the middle value in the data set, and the mode is the most common value in the data set. The range is simply the difference between the highest and lowest values in the data set.

Mean Definition

The mean is the arithmetic average of a set of numbers and is often used as a measure of central tendency. The median is the middle value in a set of data, while the mode is the most frequently occurring value. The range is the difference between the highest and lowest values in a set of data.

Median Definition

The median is the number that is in the middle of a set of numbers. To find the median, you first need to order the numbers from least to greatest. Then, if there is an odd number of numbers, the median is the middle number. If there is an even number of numbers, the median is the mean of the two middle numbers.

For example, let’s say you have the following set of numbers: 3, 7, 9, 10

First, you would order them from least to greatest: 3, 7, 9, 10

Since there are four numbers in this set, we need to find the mean of the two middle numbers. The two middle numbers are 7 and 9. To find their mean, we add them together and then divide by 2: (7 + 9) / 2 = 16 / 2 = 8

Therefore, 8 is the median of this set of numbers.

Mode Definition

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

For example, if we have the following set of numbers: 1, 3, 6, 6, 6, 7, 7

The mode would be 6 because it occurs more often than any other number. If there are two numbers that occur equally often, we say that the set has two modes. For example: 1, 2, 2, 3

Both 2 and 3 occur twice, so the set has two modes. Sometimes a set of data can have no mode. This happens when there is no value that occurs more often than any other.
An example where there is no mode: 5, 9, 11, 23

Range Definition

The range is the difference between the highest and lowest values in a data set. To find the range, first order the data from least to greatest value. Then, subtract the smallest value from the largest value. The resulting number is the range.

For example, let’s say we have the following data set: 2, 4, 7, 9

To find the range, we would first order the data from least to greatest value: 2, 4, 7, 9

Then, we would subtract the smallest value (2) from the largest value (9): 9 – 2 = 7

Therefore, the range for this data set is 7.

Which is best to use?

There are multiple measures of central tendency, but which one is best to use depends on the data set. For example, if there is a data set with outliers, then the median would be the best measure of central tendency to use because it is not influenced by outliers. If there is a data set with equally distributed values, then the mean would be the best measure of central tendency to use.

Comparing Mean, Median, Mode and Range

Comparing Mean, Median, Mode and Range:

When it comes to statistics, there are a lot of different concepts and terms that you need to know. It can be difficult to keep everything straight in your head, but if you’re struggling with the basics, everything else will seem even more confusing. We’re going to focus on four key concepts – mean, median, mode and range – and explain what they each mean. We’ll also provide some examples to help illustrate these concepts.

Mean:

The mean is the average of all the values in a set of data. To calculate the mean, you add up all the values and then divide by the number of values. For example, if we have the following set of data: 1, 2, 3, 4, 5 The mean would be (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3 So the mean of this data set is 3.

Median:

The median is the middle value in a set of data. To calculate the median, you first need to order all the values from smallest to largest (or vice versa). Then you find the value that is in the middle of the set. For example, if we have the following set of data: 1, 2, 3, 4, 5 The median would be 3 (the middle value) So the median of this data set

Mode:

The mode is the most common value in a set of data. To find the mode, count how often each value occurs and choose the value that occurs most often.

Range:

The range is the difference between the highest and lowest values in a set of data. To find the range, order all the data points from least to greatest and subtract

Examples of Mean

There are many ways to calculate the mean of a set of data. The most common is to add up all the values and divide by the number of values in the set. Another way to calculate the mean is to take the median of the set, which is the middle value after all the values have been sorted from least to greatest. The mode is the most frequent value in a set and can be calculated by tallying how often each value occurs. Finally, the range is simply the difference between the lowest and highest values in a set.

Here are some examples of how to calculate the mean, median, mode, and range:

To calculate the mean of 1, 2, 3, 4, and 5:

1+2+3+4+5=15
15/5=3
Therefore, 3 is the mean of 1, 2, 3, 4, and 5.

To calculate the median of 1, 2, 3, 4:

The median is simply the middle value when all values are sorted from least to greatest. In this case, it would be 2.5 (the average of 2 and 3).

To calculate mode of 1, 2:
There are two modes in this set (1 and 2), so mode would be NA (not applicable).

To calculate range of 5-10: 10-5=5

Examples Of Median

The median is the middle value in a data set. To find the median, you must first order the data from least to greatest. If there is an odd number of data points, the median is the middle value. If there is an even number of data points, the median is the average of the two middle values.

Here are some examples of median:

If your data set is {1, 3, 5, 7}, then the median is 5.
If your data set is {1, 3, 6, 7}, then the median is (3+6)/2 = 4.5.

Examples Of Mode

There are three main types of averages: mean, median, and mode. Here are some examples of each:

Mean: To calculate the mean, add up all the numbers in a data set and then divide by the number of items in the set. For example, if there are five numbers in a set (1, 2, 3, 4, 5), the mean would be ((1+2+3+4+5)/5), or 3.

Median: To find the median, first sort the data set from smallest to largest. Then, if there is an odd number of items in the set, the median is the middle item. If there is an even number of items in the set, the median is the average of the two middle items. For example, if a data set contains six numbers (1, 2, 3, 4, 5, 6), then the median would be ((3+4)/2), or 3.5.

Mode: The mode is simply the most frequently occurring number in a data set. For example, if a data set contains six numbers (1, 2, 2, 3, 4, 5), then the mode would be 2 since it occurs more often than any other number.

Examples of Range

There are three main measures of central tendency: mean, median, and mode. Range is a measure of dispersion, or how spread out the data is.

Range can be calculated by finding the difference between the highest and lowest values in a data set. For example, if we have the following data set:

1, 3, 5, 7, 9

The range would be 9 – 1 = 8. The range gives us a quick way to see how spread out the data is.

Another way to calculate range is to find the interquartile range. This is done by finding the difference between the first quartile (Q1) and third quartile (Q3). Q1 is the 25th percentile, and Q3 is the 75th percentile. To find these values, we first need to order our data from smallest to largest:

1, 3, 5, 7, 9

Next, we find the median (the middle value), which in this case is 5:

1 , 3 , 5 , 7 , 9

Now we have two halves of our data set:

1 , 3 | 5 , 7 , 9

Conclusion

There you have it! The definitions for mean, median, mode, and range, along with examples to help you better understand each concept. These are all important mathematical concepts that are often used in data analysis, so it’s definitely worth taking the time to familiarize yourself with them. If you ever need a refresher on any of these topics, be sure to refer back to this article.