How to Figure Out the Mean, Mode & Median

Learn basic mathematical equations such as the mean, median and mode.

You may think that the simple math equations you learned back in high school were only useful for helping you pass the class, but you'd be wrong. By knowing how to find the mean, median and mode, you can become a smarter shopper, an effective marketer, even a better salary negotiator, among many other things.

Things You'll Need

• Calculator

Instructions

Solving for the Mean

1. Identify all the numbers in a data set. There can be any amount of numbers in your set, and repetition of the same numbers is allowed.

2. Add up all of the numbers in the data set.

3. Divide the sum by the total amount of numbers that were added together. For example, if you had a set of five numbers containing 2, 3, 5, 7 and 8, you would add all of those numbers up (2 + 3 + 5 + 7 + 8 = 25) and divide by the amount of numbers (in this case, there are five). This gives you an equation of 25 / 5, which equals 5. Five is the mean.

Solving for the Median

1. Identify all the numbers in a data set. Again, you can have any amount of numbers in the set, and repetition of the same numbers is allowed.

2. Arrange all of the numbers in the data set from least to greatest. For example, if you had a set of five numbers containing 8, 4, 7, 2 and 5, you would arrange them like so: 2, 4, 5, 7, 8.

3. Identify the number that lies exactly in the middle of the arranged numbers. Because the number "5" is in the middle, with two values to the left and two values to the right, five is the median. This way of finding the median is only effective if there is an odd amount of numbers in a data set. If you are dealing with a set of data that contains an even amount of numbers, proceed to Step 4.

4. Find the median for an even amount of numbers by calculating the mean of the two numbers in the middle of the data set. For example, if you have a set of six numbers that includes 2, 4, 4, 6, 8 and 9, you would get the median by adding 4 + 6 = 10 (because they are the two numbers in the middle of the data set) and dividing that sum by two, which equals five (10 divided by 2). Five is the median in this example.

Solving for the Mode

1. Arrange all of the numbers in the data set from least to greatest.

2. Determine which number or value occurs the most. That value is considered to be the mode. For example, if you have a set of seven numbers that includes 5, 7, 6, 2, 6, 5 and 6, find the mode by arranging the numbers from least to greatest--that is, 2, 5, 5, 6, 6, 6 and 7. Because the number "6" occurs the most frequently, six is the mode.

3. Verify that there is a number from the data set that occurs more than once. If none of the numbers occurs more than once, then there is no mode. Also keep in mind that it is possible to have more than one mode, assuming there is a tie with the number or numbers that occur most frequently.

Tips & Warnings

• Remember that it doesn't matter if numbers are repeated in the various data sets. Each number counts separately, no matter how many times it's repeated.

• When solving for the mean or median, it is possible to end up with a fraction or decimal; this is OK.

• Do no confuse the mean with the median; they both represent different values of numbers.

References

• Regents Exam Prep Center: Measure of Central Tendency

Resources

• Purple Math: Mean, Median, Mode and Range