How to Calculate Median Values in Data Sets (With Tips and Examples)
By Indeed Editorial Team
Updated September 7, 2022
Published November 5, 2021
The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.
When analyzing data sets at work, you may need to find the median, which is the middle figure of a group of numbers. Fortunately, finding the median is easy when you use specific counting methods and equations. Once you understand how to calculate the median from a group of numbers, you can use it to analyze your data and averages. In this article, we explore what a median is, explain how to calculate it, and give you examples and tips for finding the median.
How to calculate median values for odd-numbered data
Before you can determine how to calculate the median values of your data set, learn the number of data points you have. Count the data you have and then:
1. Arrange your numbers in order
Start by ordering the numbers in your data set from lowest to highest. For example, if your original data set looks like this: 10, 8, 6, 9, 2, 3, 4, 5, 8, rearrange it to look like this: 2, 3, 4, 5, 6, 8, 8, 9, 10. Count how many numbers you have in your set, as you need this number to calculate the median.
2. Find the number in the middle
One way to find the median is to find the number in the middle of the set, which is easy with odd-numbered data. In the example above, the median is 6. If you have a large data set, finding the middle number requires a more advanced calculation. Instead, you can use: (n + 1) / 2. In this equation, N is the number of points in the data set.
Using the example from above again, there are nine numbers in the data set. When you put 9 into the equation, it looks like this: (9 + 1) / 2 = 5. This means the median is the fifth number in the data set, which is 6 in the example set above.
Why calculate the median?
The median is the middle, centre or the halfway point of a group of numbers. When you order a set of numbers from lowest to highest, the median is the number directly in the middle. 50% of the values in a set occur below the median, and 50% are above the median.
Two related statistical figures that people often confuse with the median are:
Mean, a data set's average: To calculate the mean, you add all the numbers in a set together and divide the total by the number of values in the set. For example, if your data set is: 3, 4, 7, 9, the total is 23 and when you divide that by four, your mean is 5.75.
Mode, the most common number in a data set: It occurs more frequently than any other figure. For example, if your data set is 1, 3, 4, 4, 7, 8, 9, the mode is 4.
You might choose to find a data set's median rather than its mean or mode to avoid outliers or disproportionately low or high numbers in your statistical analysis. Outliers can create an average that doesn't accurately represent a group of numbers. Therefore, the median is sometimes the more accurate figure to use in your analysis.
How to calculate median values for even-numbered data
Calculating the median for even-numbered data is more complex, as there are two numbers in the middle. If your data set includes an even amount of numbers, such as a data set that only includes two data points, follow these steps to find the median:
1. Arrange your numbers in order
Arrange your even-numbered data set in order from lowest to highest. Then, count how many numbers you have in your data set. This number should be even to move on to the next step.
2. Find the pair of numbers in the middle
As your data set includes an even amount of numbers, there are two numbers in the middle. Once your numbers are in order, you can look for those two middle numbers. For example, if your data set is: 15, 16, 17, 18, 19, 20, the two numbers in the middle are 17 and 18.
Instead of manually finding the two middle numbers in large data sets, use the following equations: n / 2 and n / 2 + 1. N is the number of points you have in your data set. For example, there are six numbers in the data set above, so the equations would look like this: 6 / 2 = 3 and 6 / 2 + 1 = 4. This means the third and fourth numbers of the data set are the middle pairs.
3. Find the pair's average
Using the two numbers in the middle, calculate the average to find your median. To calculate the average, add your two middle numbers together and divide them by two. Using the example above, 17 + 18 = 35 and if you divide that by 2, you find a median of 17.5.
How to find the median for ordinal data
If you have data that doesn't include numbers but is organized by category instead, it's ordinal data. An example of an ordinal data set is: disagree, somewhat disagree, neutral, somewhat agree, and agree. Here's how you can find the median for ordinal data:
1. Order the data
Order the data in a way that makes sense to the category, such as lowest to highest, which would be disagree to agree in the above example. Then, determine how many data points you have to see if you have an odd or even number. If you have an even number, you can't accurately calculate the median as there won't be an average between ordinal data points. If you have an odd number, you can move on to the next step.
2. Calculate the median
To calculate the median of an odd ordinal data set, use the (n + 1) / 2 equation. Remember that n stands for the number of data points you have. For example, if your data set is slow, medium, fast, your equation would be (3 + 1) / 2 = 2. This means the second item in your data set, in this case, medium, is the median.
Examples of how to find the median
To help you better understand how to find the median of any data set, consider the following examples:
Odd-numbered data set example
Example: Find the median of 3, 15, 9, 2, 27, 24, 38, 26, 45, 21, 56, 16, 11, 55, 29, 22, 60.
Order the numbers from lowest to highest: 2, 3, 9, 11, 15, 16, 21, 22, 24, 26, 27, 29, 38, 45, 55, 56, 60.
There are 17 numbers, so the middle number, or median, is the ninth value: 24.
Using an equation: (17 + 1) / 2 = 9
Even-numbered data set example
Example: Find the median of 12, 3, 5, 9, 22, 37, 44, 51, 32, 2, 10, 25.
Order the numbers from lowest to highest: 2, 3, 5, 9, 10, 12, 22, 25, 32, 37, 44, 51.
There are 12 numbers, so the middle numbers are the sixth and seventh values, or 12 and 22.
Using an equation: (12 / 2) = 6 and (12 / 2) + 1 = 7
Average the sixth and seventh values to find the median: (12 + 22) / 2 = 17
Ordinal data set example
Example: Find the median of agree, disagree, somewhat agree, strongly disagree, somewhat disagree, strongly agree, neutral.
Order the values from lowest to highest: strongly disagree, disagree, somewhat disagree, neutral, somewhat agree, agree, strongly agree.
There are seven values, so the middle value, or median, is the fourth value: neutral.
Using an equation: (7 + 1) / 2 = 4
Tips for finding the median
When working with medians, consider the following tips:
Always put your data set in ascending order for an accurate result.
When working with a large data set, use equations to find the median easily.
If you want to find the median of an even-numbered data set, convert each value to a number first. This is not a completely accurate result, but it can be a good way to analyze ordinal data.
Write your data down in order and cross out a number from each side to find the median efficiently.
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