Numbers and groups of numbers are all around us.

For example, what is the total number of students at your school?

Who is the oldest student or the youngest student?

Who runs the fastest mile and who has the highest test average?

A** measure of central tendency** is one way to organize data so you can figure out what it is telling you.

Three **Measures of Central Tendencies **include: MEAN, MEDIAN & MODE.

A measure of central tendency is a single number that is used to summarize all the values of a data set.

For example, you have this group of people. You may want to know if they are all close to the same age, or what is the average height or how many have dark hair ?

**Let’s work an example.**

What is the mean median and mode of this family?

The ages are 68,10,7,40,36,2.12,65

MEAN - the average of a set of numbers.

Mean and average are the same.

STEPS FOR CALCULATING THE MEAN:

1. Add all of the numbers in the data set

2. Divide by the total number of items in the data set

3. If there is a ZERO, it must be included!

**mean**of the average ages of the family.

Let’s add the ages together 68,10,7,40,36,2.12,65 = 240

Now let’s divide by the number of numbers in the data set.

If there was a zero it would be included and we have 8 members.

So 240 divided by 8 = 30 so the average age is thirty

**Now let’s calculate median**

MEDIAN - the number in the center of a data set when the numbers are in order from least to greatest.

STEPS TO DETERMINING THE MEDIAN:

1. Arrange the numbers from least to greatest order.

2. Cross off the greatest and least numbers in the list (at the

same time) until you are left with just one number in the

middle - this is the MEDIAN!

3. If there are two numbers left in the middle, you have to find

the MEAN or AVERAGE of the two numbers.

Find the median of the ages of the family.

68,10,7,40,36,2.12,65

Let's arrange from least to greatest

Since we have an even number we need to take the average of the numbers in the middle.

So the mean or average of 12 and 36 is 48 divided by 2 which equals 24.

If you had an odd number it would just be the number in the middle.

**Mode **equals the number which occurs most often in a data set. There might be one mode, no mode, or many modes.

Arrange the numbers from least to greatest order.

See if any numbers repeat.

The number that repeats most often is the mode.

**What is the mode of the family?**

Let’s arrange from least to greatest

**2,7,10,12,36,40,65,68**

So no number repeats so you have **no mode.**

If you had this,

**2,7,7,7,10,12,36,40,65,68**

Then 7 would be the mode.

Finally let’s figure out the** range **for this data set.

RANGE is NOT a measure of central tendencies, it is a MEASURE OF VARIATION.

It is a measure of the variation between the greatest and lowest numbers in a data set.

Find the greatest number and SUBTRACT the least number.

**What is the range of of the family?**

Let"s order from least to greatest.

**2,7,10,12,36,40,65,68**

So the range is 68 -2 which equals 66

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