How to Calculate Mean Median Mode and Range

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.

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!

Let’s calculate the mean of the family’s ages.

Let’s add the numbers together.

68 + 10 +7 + 40 + 36 + 2 + 12 + 65 = 240

Now let’s divide by the number of numbers in the data set. Remember, if there was a zero it would be included. There are  8 family members.

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

Now let’s calculate median.

central tendency

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!
  1. 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

 

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

2,7,7,12,40,48

Then 7 would be the mode.

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 – how much data VARIES between the greatest and least values.

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

Steps to Calculate Range

Arrange the data from least to greatest.

Find the greatest number and SUBTRACT the least number.

The difference between these two numbers is your range.

EXAMPLES:

What is the range of of the family?

Lets order from least to greatest

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

So the range is 68 -2 which equals 66.