Measures of Central Tendency

What Are Measures of Central Tendency?

By Measures of Central Tendency, we are referring to a variety of measurements of a set of data.

What Are Measures of Central Tendency? Each of these measurements will result in a single number that represents the data set in a specific way.

There are 3 Measures of Central Tendency

These are:

Mean Mean

These are: Mean Mean Median Median

These are: Mean Mean Median Median Mode Mode

Let’s begin with an explanation of Mean

Mean The Mean of a set of data is the average value of all of the numbers in the set.

Mean For example, let’s consider this set of numbers: {4, 7, 9, 11, 14}

Mean First, add up all of the numbers in the set = 45

Mean {4, 7, 9, 11, 14} Next, count the “number of numbers” in the set. There are 5 numbers in this set.

Mean {4, 7, 9, 11, 14} Finally, divide the sum of all the numbers in the set by the “number of numbers” in the set = 45 There are 5 numbers in this set. 45 ÷ 5 = 9

Mean {4, 7, 9, 11, 14} 45 ÷ 5 = 9 The mean of this set is equal to 9

Mean Now, try one on your own: Determine the mean of this set of data: {12, 15, 22, 25, 36, 40}

Mean The mean of this set of data is:

Mean CORRECT! {12, 15, 22, 25, 36, 40} The mean of this set of data is: 25

Mean Sorry, but that’s not quite right. Perhaps a little review would help.

Next Step Now that you have a good understanding of mean, let’s go on to the next Measure of Central Tendency which is the Median

Median Think about driving down the interstate. Most of the time, there is an area of grass between the two strips of highway. This grassy area is called the median because it is in the middle of the interstate

Median In a similar way, the median of a set of numbers is the number that is exactly in the middle of the set.

Median Example Consider again this set of data: {4, 7, 9, 11, 14}

Median Example {4, 7, 9, 11, 14} The number 9 has two numbers to its left and two numbers to its right, so it is in the middle of this set of data.

Median Example {4, 7, 9, 11, 14} Since the number 9 is in the middle of this set of data, 9 is the median.

On Your Own Try a problem where you determine the median of a set of data on your own now.

Try This One Determine the median of this set of data: {3, 6, 12, 19, 23, 29, 32}

Try This One {3, 6, 12, 19, 23, 29, 32} The median of this set of data is:

Good Job! Correct! The median of this set of data is 19 Now let’s continue …

Ascending Order {3, 6, 12, 19, 23, 29, 32} One thing that you may notice about the set of data you just worked with is that it is already arranged in ascending order.

Ascending Order {3, 6, 12, 19, 23, 29, 32} This means that the numbers start from the smallest. The next one is the next largest, and they continue on this way to the largest one.

Ascending Order When calculating mean or mode, the order of the data doesn’t matter. However, when calculating median, the numbers must be in ascending order.

Example of Ascending Order You’ll notice that the set of data below is not in ascending order. {14, 2, 47, 32, 12, 53, 29}

Example of Ascending Order To find median, we must place these numbers in ascending order: {14, 2, 47, 32, 12, 53, 29} equals: {2, 12, 14, 29, 32, 47, 53}

Example of Ascending Order The middle number of this set, or the median, is the number 29. {2, 12, 14, 29, 32, 47, 53}

Practice Now try another one on your own.

Practice Determine the median of the following set of data: {41, 13, 63, 28, 4, 55, 30}

Practice The median of this set of data is:

Good Job! Correct! The median of this set of data is 30

An Even Number of Numbers So far, all of the data sets we have looked at to determine median have contained an odd number of terms, or numbers. It is very easy to find the middle number in a set if the number of terms is odd.

An Even Number of Numbers Sometimes though, the number of terms in a set is even. This requires some additional thought to determine the median of such a set.

An Even Number of Numbers For example, consider this set of data: {2, 5, 8, 12, 13, 16}

An Even Number of Numbers {2, 5, 8, 12, 13, 16} First of all, these numbers are in ascending order, so we don’t have to worry about that. However, there is no number directly in the middle of the data set!

Finding the Middle Number {2, 5, 8, 12, 13, 16} When there is an even number of terms in a data set, we must find the middle two numbers. In this case, the two numbers in the middle are 8 and 12.

Finding the Middle Number {2, 5, 8, 12, 13, 16} To determine the median of this set of data, we now take the two middle numbers and find the mean of those.

Finding the Middle Number {2, 5, 8, 12, 13, 16} The two middle numbers are 8 and 12. Find the mean of 8 and 12: = ÷ 2 = 10

Finding the Middle Number {2, 5, 8, 12, 13, 16} = ÷ 2 = 10 The median of this set of data is 10.

Practice Now, try one on your own.

Practice Determine the median of this set of data: {5, 8, 13, 20, 24, 34, 42, 57}

Practice The median of this set of data is:

Good Job! Correct! The median of this set of data is 22 {5, 8, 13, 20, 24, 34, 42, 57}

Moving On … Now that you have a good grasp of the concepts of mean and median, let’s learn about the mode of a set.

Mode The mode of a set is the number that appears most often in a set of data.

Mode The word mode begins with the letters m and o … The word most also begins with the letters m and o Mode = Most

Example of Mode {16, 9, 2, 9, 8, 11, 9, 13, 11} In the data set above, you will notice that the number 9 appears more often than any other number. 9 appears most often. 9 is the mode of this set. (You may also notice that the order of terms did not matter)

Practice Finding the Mode Now, try one on your own.

Practice Finding the Mode Determine the mode of the following set of data: {31, 64, 89, 64, 31, 102, 31, 29}

Practice Finding the Mode {31, 64, 89, 64, 56, 31, 102, 31, 29,} The mode of the set of data is

Good Job! Correct! {31, 64, 89, 64, 56, 31, 102, 31, 29,} The mode of this set of data is 31

Congratulations! You have mastered the 3 Measures of Central Tendency: Mean, Median, and Mode.

Not Quite! Sorry, but that’s not quite right. Perhaps a little review will help.

Not Quite! Sorry, but that’s not quite right. Perhaps a little review will help.

Not Quite! Sorry, but that’s not quite right. Perhaps a little review will help.

Not Quite! Sorry, but that’s not quite right. Perhaps a little review will help.

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