Measures of Center - Lesson

Measures of Center and Variability

What are measures of center/variability?

In 6th grade, you were introduced to mean, median, mode, range, and interquartile range (IQR). These are statistics that serve as measures of center or variability. Measures of center give you an understanding of the middle number that represents the data. The measure of variability describes how much of a difference there is between the numbers in the data set.

Let's review each of these...

Fill in the Blanks

To calculate the mean, divide the sum by the number of data points. What is the mean of this data set?

7, 9, 4, 8, 7

Fill in the Blanks

Let's try another one. Remember, to calculate the mean, divide the sum by the number of data points. What is the mean of the data set?

6, 1, 3, 4, 1

Fill in the Blanks

What is the mean of this data set?

8, 13, 2, 1

Reorder

Now let's find the median (the medium/middle number). The first step is to place all the data points in numerical order.

7, 9, 4, 8,

• 4

• 6

• 7

• 8

• 9

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

With the numbers in order, you should now be able to see the median by counting from the outsides until you get to the number in the middle. What is the median?

4, 6, 7, 8, 9

• 4

• 7

• 8

• 9

• 6

​Before we move on, let's make sure we remember that if there are two numbers in the middle and we're asked to find the median:

1. If the two middle numbers are the same. Just give that number.

2. If the two middle numbers are different, add them and divide by 2 (that's the same as finding the mean).

Fill in the Blanks

What is the median of the following data set?

25, 26, 27, 27, 30, 30

Fill in the Blanks

What is the median of the following data set? (Remember to add the two middle numbers and then divide the sum by 2)

25, 26, 27, 28, 30, 30, 32, 35

Fill in the Blanks

What is the median of this data set? Remember to put the numbers in order first.

1, 5, 8, 3, 1, 9

Fill in the Blanks

The mode is the number that shows up the most in the data set. What is the mode of this data set?

28, 25, 30, 26, 27, 30,

Multiple Select

There can be multiple modes if they each show up the most. Which quantities are modes?

28, 25, 30, 26, 27, 30, 25

• 25

• 26

• 27

• 28

• 30

Fill in the Blanks

To get the range, subtract the highest and lowest numbers in the data set. What is the range of the data set?

28, 25, 30, 26, 27, 30, 25

Fill in the Blanks

What is the range of this data set?

32, 50, 48, 90, 65, 40

​The interquartile range (IQR) represents the middle 50% of the data. To calculate the IQR,

1. Put the data in order

2. Split the data in half

3. Find the medians of the left (Q1) and the right (Q3).

4. Subtract Q3-Q1

​but we'll come back to this in a later lesson...

​It doesn't always make sense to calculate or use all the measures of center or variability for every data set.

Back to appropriate measures...

To determine which measure of center or variability should be used, you can simply look at the distribution of the data.

When to use the mean and range...

​The mean and range are used when the data is evenly distributed or symmetrical. The only distinction is there cannot be any outliers.

​Even distribution with no outliers = YES

​Even distribution with outliers = NO

Multiple Select

When are the mean and range the most appropriate measure of center/variability? (There are 2 correct answers.)

• When the data is evenly distributed

• When the data is symmetrical

• When the data leans more to the left or the right.

• When the data has an outlier.

When to use the median or IQR...

If the data is either uneven, or skewed (leaning to the left or right), has an outlier, or both, you need to use the median or interquartile range (IQR).

Multiple Select

When are the median and IQR the most appropriate measure of center/variability? (There are 2 correct answers.)

• When the data is evenly distributed

• When the data is symmetrical

• When the data leans more to the left or the right.

• When the data has an outlier.

​	Measure of Center	Measure of Variability
Evenly distributed, clustered together, and no outlier	​Mean	​Range
Skewed, or with an outlier	Median	​IQR

​Long story short...

Multiple Select

This data is evenly distributed with no outlier. Which two measures of center and variability are appropriate?

• range

• median

• mean

• iqr

Multiple Select

What are the most appropriate measures of center and variability?

• range

• median

• mean

• iqr

Multiple Select

What are the most appropriate measures of center and variability?

• range

• median

• mean

• iqr

Multiple Select

This data has an outlier. Which measures of center and variability should be used?

• range

• median

• mean

• iqr

You're all done. Now apply your new found understanding of measures of center as soon as you can.

​

Great job!!!