How to Find the Mean, Median and ModeAll Posts
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We all remember learning about these terms in math class. But what exactly they are and how to find them is difficult to remember.
Trust me, you’re not alone if you think that!
Math is not easy, and if your child is struggling in math class or feeling math anxiety, they’re not alone.
This article will give you a quick rundown of how to quickly find the mean, median and mode in a data set and examples of when you might need to find these arithmetic means.
If you’re not feeling like an expert by the end of the article, we’ve also got some great resources that you can check out for extra help.
Measures of central tendency
The mean, median and mode are all “measures of central tendency”. That sounds complex but it just means the different middle points of a set of data.
While each one tells us a middle point, they are all different.
So, what is the difference between the mean, median and mode? The mean is calculated to find the average value of the data. The median is the number in the middle of the data set. And the mode finds the most common number in a list of numbers.
Some of the calculations can be affected by outliers or the range of the data set. So, a lot of times one value is a lot more useful than the other two.
How to find the mean
The mean, also called the average, is calculated by adding together all of the numbers and then dividing by the number of values in the set.
How exactly do you do this? Keep reading and we’ll give you a step-by-step example.
1. What is the mean?
It’s important to first understand what the mean actually is. When there is a particular set of data, the most common value that people want to know about it is the mean or the average. The mean of a data set uses all of the data points to determine what all the values average out to.
2. Step-by-step instructions
Now, how is the mean found? Here are step-by-step instructions that can be used to find the mean of any group of numbers.
Let’s start with a data set. Our numbers will be 2, 7, 9, 12, 13, 13 and 21.
First, we will find the total number when all of these values are added together.
Then, we count up the number of values in our data set. In this example, there are 7 values. So, we divide the total number by 7.
And that’s it. You’ve found the mean!
How to find the median
The median is found by listing the values from smallest to largest and then finding the number in the middle.
1. What is the median?
The median is the number in the middle of a set of values. Sometimes, it is called the midpoint of the data.
2. Step-by-step instructions
Finding the middle value of a data set always starts with organizing the numbers from smallest to largest. While it’s possible to find the median in an unorganized set of data, it’s much more difficult.
To start, we’ll use the same data set as above: 2, 7, 9, 12, 13, 13 and 21.
Since these numbers are already lined up from smallest to largest, it’s easier to see which one is the middle number. The median is 12.
That data set was also easier because it had an odd number of variables. What happens if there’s an even number of values?
Let’s say the data set is 5, 9, 11, 11, 17, 19, 22 and 25. When we count to the middle, we find that 11 and 17 are the two numbers in the middle. Next, we add these two numbers together.
Then, we divide by 2 to find the middle of these two numbers.
So, for this data set, 14 is the median.
How to find the mode
The mode is the most common value seen in a set of data.
1. What is the mode?
Many sets of data have values that are repeated multiple times. The mode is the value that is repeated with the most frequency.
2. Step-by-step instructions
The easiest way to find the mode is to organize the data values in an ascending or descending order. Organizing the data in this way will also help you see any outliers.
In our data set, 2, 7, 9, 12, 13, 13 and 21, there is only one value that is repeated more than once. Since 13 is seen twice, it is the mode.
In the second set of data we looked at, finding the mode is very similar.
5, 9, 11, 11, 17, 19, 22 and 25
11 is seen with the most frequency, so it is the mode.
Applying the mean, median and mode
While mean, median and mode may seem like abstract math concepts, they actually have a lot of applications in the real world.
These values are used by researchers to understand the data that they collected. It’s used by marketers to understand what advertisements are performing well and which ones aren’t. It’s used by those in real estate and they determine the average price of a home in a particular market.
It’s likely that you even use mean, median and mode calculations in your daily life without realizing it.
You may calculate how many miles you drive on an average day and the average gas mileage in your car to know if you need to go to the gas station today or tomorrow. In this case, you’ll find the mean of the miles you drive per day and the mean of the gas mileage your car typically gets.
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Example problem 1: Chicken nuggets
You may think back on the average number of chicken nuggets each of your kids eat before deciding how many to cook for lunch today. Some days they may eat two while other days they eat six. So you’ll likely choose to use the mode and make the amount they most commonly eat.
In some cases, it’s easy to determine whether you should find the mean, median or mode. Other times, it’s helpful to ask, ‘Are there a few outliers?’
Like in the chicken nugget example, Susy might have eaten 6 chicken nuggets yesterday, but you know that’s not typical, so you use the mode, or the number that she’s eaten the most often, instead.
It can also be helpful to ask, ‘Is there a big range in the numbers?’ This is asking if there is a big difference between the largest and smallest numbers in the data set. If there’s a big range, with many numbers filling in the space between, that can change which mean formula you use.
Example problem 2: Salaries
Another common place to use these formulas is when talking about salaries. Let’s analyze a data set together to understand when you would use the mean, median, and mode.
At one company, the annual salaries are in the thousands but we’ll take out the zeros for this example.
Our numbers are 28, 29, 30, 30, 30, 31, 33, 35, 42, 45, 45, 47, 54, 88, 97, and 185.
This data set represents employees that are new to the company, all the way up to those in senior leadership positions.
To calculate the mean, we add together all the numbers equaling 849. Then we divide by the number of values in the set. 849/16=53
Our numbers are already in ascending order to calculate the median and mode. The median is found by going to the number in the middle. In this set, it’s the numbers 35 and 42. So we add those two numbers together and then divide by 2.
The mode is found by looking for the number with the highest frequency. In this data set, it is 30, which is seen three times.
Because there is such a wide range of numbers in this data set, the different values allow us to see differences. The mean shows the average income of an employee, but it is skewed high because of the high salaries of those at the top.
The median is closer to what most employees experience in the company. It takes out the really high and low numbers so that you can better understand what most people in that company make.
The mode is useful in understanding what is a commonly experienced salary in the company. If you were looking at applying for this job, you could know that this is a salary you would be likely to be offered.
Finding the mean, median and mode using negative numbers and decimals
When a data set contains negative numbers and decimals it can seem extra tricky. However, the process stays the same. And especially if you are using a calculator, it’s not much more difficult to do.
Extra resources to help you
There are plenty of resources out there to help you support your child or students in calculating mean, median and mode. Check out these examples:
- Try using a mean median and mode calculator.
- Use Excel or Google Sheets, where your students can type in the formula for finding the mean, median or mode, and the software will do the work for them.
- Use a statistics calculator to find the mean, median and mode.
- Look up online worksheets that provide examples, visuals and detailed instructions on how to do these formulas.
- Prodigy's blog covers plenty of other math topics, including everything from free math resources to the best math puzzles.
If you're looking for an engaging way to help your student or child master math concepts like mean, median or mode, try Prodigy Math! The game-based learning platform covers thousands of math skills from 1st-8th grade, including Common Core content. And with teacher and parent integration, it's a great way to engage students in math both in the classroom and at home.
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