Mean, Median, Mode: What are they and how to find them?

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When you take the SAT or the ACT, you will encounter some statistics questions on the math sections. These questions typically ask you to find the mean, median, or mode of a data set.

To earn a perfect score on the SAT or ACT Math sections, it is critical that you know the definitions of these terms as well as how to calculate them in a short amount of time. Even if you’re already familiar with mean, median, and mode, you’ll likely want a refresher before you take your standardized test.

This Prep Expert guide will walk you through everything you need to know about mean, median, and mode before you take the SAT or ACT. As always, if you want additional tips and strategies about taking these tests, feel free to check out the resources on our website.

What is a mean, median, and mode?

Before you learn how to calculate the mean, median, and mode of a data set, you’ll need to know what these terms mean.

Mean

A mean is a number that reflects the average of a group of numbers. When given a data set and asked to find its mean, you just need to find the statistical average.

To find the statistical average of a group of numbers, you need to follow two steps:

  1. Find the total sum of all the numbers in the data set
  2. Divide your answer for step one by the total amount of numbers in the data set.

For example, say you have a table of five numbers: 

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mrs. Pran 32
Mr. Smith 32
Ms. VanHaven 36

In the table above, these numbers represent the total number of students in various teacher’s classes: 35, 33, 32, 32, and 36.

If someone were to ask you to calculate the mean of these numbers, or the average number of students in a class, you would first add the total number of students.

35+33+32+32+36= 168

Once you’ve calculated the total sum of the numbers in the table, you would then need to divide this sum by the total amount of numbers provided in the table.

In the example above, this would be 5, since there is a number for each of the five teachers’ classes.

168/5= 33.6

This means that the mean for this data set is 33.6.

Median

The median of a data set is the number that is directly in the middle of the data set after the numbers in that set have been put in order from least to greatest.

Finding the median of a data set involves more than just guessing what number is halfway between the highest and lowest values of the data set. It requires a couple of steps:

  1. Arrange the numbers in the data set from least to greatest
  2. Cross off numbers from your data set, one at a time, alternating between the least and greatest values until you have a single value in the middle

Note: If the data set has an even amount of values, calculate the mean of the remaining values to determine the median

Let’s look at the values from the example earlier:

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mrs. Pran 32
Mr. Smith 32
Ms. VanHaven 36

To find the median of these numbers, we first need to put them in order. That would leave us with 32, 32, 33, 35, and 36.

Now that these values are in order, we need to cross off the values from either side until we have one value remaining in the middle:

32, 32, 33, 35, 36

32, 32, 33, 35, 36

32, 32, 33, 35, 36

32, 32, 33, 35, 36

Completing this step would leave us with 33 as the median for this data set.

While this worked out smoothly because there were an odd number of values in this data set (5), calculating the median with an even data set requires one more step.

Let’s say there was an additional class that wasn’t listed before, giving us a new data set:

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mr. Thompson 34
Mrs. Pran 32
Mr. Smith 32
Ms. VanHaven 36

First, we need to put our values in order: 32, 32, 33, 34, 35, 36.

Then, we need to cross values of alternating sides until we are left with two values in the middle.

32, 32, 33, 34 35, 36

32, 32, 33, 34, 35, 36

32, 32, 33, 34, 35, 36

32, 32, 33, 34, 35, 36

Finally, we need to calculate the mean of these two values (33 and 34) to determine the median of this data set. 

To do this, we add 33 and 34 and divide the sum by 2, since there are two values that we are using to calculate the mean. 

33+34= 67. 

67/2= 33.5

This would mean that 33.5 is the median of the data set in this second example.

Mode

The mode of a data set is the number which appears the most. Sometimes, a data set can have more than one mode, and sometimes it can have no mode at all.

If there are no values that repeat within a data set, there is no mode. If two different values repeat the same number of times, there are two modes.

Consider the class size example we used above:

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mr. Thompson 34
Mrs. Pran 32
Mr. Smith 32
Ms. VanHaven 36

The mode of this data set is 32, since Mrs. Pran and Mr. Smith each has 32 students in their classes, and this value is repeated more than any other value in the table.

If we were to look at different teachers’ class sizes in a different data set, we might have a different result:

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mr. Thompson 34
Mrs. Pran 32
Ms. Mark 33
Mr. Smith 32
Mrs. Spring 31
Ms. VanHaven 36

For this example, there are two modes: 32 and 33, since both of these values repeat the same number of times.

Let’s look at one more example:

Teacher Name Number of Students in the Class
Mr. Jones 35
Ms. Jackson 33
Mr. Thompson 34
Mrs. Pran 32
Ms. Mark 33
Mr. Smith 32
Mrs. Spring 31
Ms. Erickson 32
Ms. VanHaven 36

For this example, the mode is 32. Even though both 32 and 33 are values that are repeated in this data set, 32 is repeated the most.

Next steps

Now that you know how to determine the mean, median, and mode(s) of a data set, you will be more comfortable addressing these types of statistics questions on the SAT or ACT.

For additional practice or help with these terms or any other math concepts, sign up for an SAT or ACT prep course or work with one of Prep Expert’s highly qualified, private math tutors. Learn more today when you visit our website.






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