## Measures of Mean, Median, Mode, and Range

#### Aligned To Common Core Standard:

**Grade 6 Statistics** - 6.SP.B.5c

What Are The Measures of Mean, Median, Mode, and Range?
The four primary measures we commonly use that provide us with statistical information about a set of data are the mean, median, mode, and range. Information about these measures tells you how the set of data points are connected. Mean, Median, Mode, and Range are also generally known as 'measures of central tendency.'
**Mean** - First is the mean, which means average. It is calculated by adding all the numbers given in a question and then dividing the sum by the number of addends.
Take a look at this example; 16, 14, 12 and 18. To find the average number or the mean, first, add all the four values together. 16 + 14 + 12 + 18 = 60
Since the data set consisted of four numbers, you divide the result with 4.
Therefore, 60 ÷ 4 = 15
**Median** - Median is a simple measure. It is the middle number when all numbers are listed in the order from least to the greatest. When the data set count is an odd number, you will have a median value. At times, the count is even, in such a case, add the middle two numbers together and divide by 2. You will get the median.
**Mode** - A mode is as simple as finding the most repeated value in the data set.
**Range** - In statistics, the range is the difference between the largest and smallest values in a data set.

### Printable Worksheets And Lessons

- A Rundown Step-by-step Lesson- Go over all the required skills for this topic area.
- Guided Lesson - Find the number needed to complete a fixed mean, median number of tractors, and nine numbers to have fun with.
- Guided Lesson Explanation - I used a lot of space to help explain. I find kids are more successful when they use an entire page to complete these types of problems.
- Practice Worksheet - We work, rework, and even over work these skills. It is an important skill.
- Mean, Median, Mode, and Range Five Pack - Breakdown each data set and find the central measures.
- Central Tendency - Mean, Mode, Median Five Pack - There is a bit more to read here.
- Mean, Median, Mode Five Pack - We create battle math sheets out of this in my class.
- Matching Worksheet - This is a great one to start class with.

#### Homework Sheets

Students dive into large data sets and they are tasked with making sense of the data.

- Homework 1 - A mean is an average. To find the mean, add up all the data you have and then divide by the number of instances of data you have.
- Homework 2 - A median is the basic center of your data set. The first step in determining the median is to rewrite the data set in ascending order (least to greatest).
- Homework 3 - The mode is piece of data item that appears most.

#### Practice Worksheets

I find this to be one of the more useful skills for students.

- Practice 1 - The "range" is just the difference between the largest piece of data and smallest piece of data.
- Practice 2 - Find the mean, median, mode, and range of the data set.
- Practice 3 - The girls were cleaning up a train. Below you see a list of the number of bags of garbage they each made on the train.

#### Math Skill Quizzes

Because of the mix of problem numbers, the scoring keys are different than all others I have presented you with.

- Quiz 1 - Nicole is reporting about the number of children the Kelly family had. She forgot the number of children one of the couples had, but she knew the mean of the entire family.
- Quiz 2 - Some children compared how many toys they have.
- Quiz 3 - Some students compared how many Bs they received on exams.

### What Do These Measures of Central Tendency Indicate In your Data Sets?

All the measures of central tendency that we were able to extract from the data in these worksheets provide us with a summary of all of our statistics. They help us define what is normal or a center point in our data. It also tells us how spread out our data is. Each individual measure we calculated above tells us the center point of the set using a slightly different means. This can help us understand our data much better and make decisions based on it. Think about how a teacher can use this to understand how difficult a test was that they administered to students. We would start by calculating the average and that is a nice measure to work off of, but it does not give us a complete picture. This just tells us that the average student scored a certain value on the exam. It does not tell us if some stellar students scored really high scores while the rest of the class faltered. If we want to understand where half the data fell off, we would go after the median. We can use this value to get an idea where our values dispersed from. If we compare these two values, we can get a much better picture of how the class did as a whole. These values would be awfully close if the class as a whole gravitated toward the average. If these values are way out of whack, they we had a number of outliers that pushed the score in one direction. A teacher wants those values to be close to indicate that the average is a valid indication of the class’s success rate.