WHAT DO THEY ALL MEAN?

All of the previous words can be summed up with the phrase

MEASURES OF MEASURES OF CENTRAL TENDENCYCENTRAL TENDENCY

MeanThis is what we usually mean when we say “What’s my average.”

We could say, “What grade do I normally get?”

How is the mean of a set of numbers found?

• Add all the numbers in the set together.• Divide the sum by the number of data items in

the set.• The quotient is the mean of the set of

numbers.• Example: 10, 18, 12 and 16

– Add 10 + 18 + 12 + 16 = 56– Divide 56 by 4– The mean is 14

Median

• Is the number that is in the middle of a set of numbers.

• Half the numbers are below the median and half the numbers are above the median

How is the median of a set of numbers found?

• Arrange the numbers in the set in order from least to greatest.

• Count in from the ends.• The middle number is the median of a set of

numbers.• If more than one number is in the middle of the

set of numbers, the mean of those two numbers is the median of the set of numbers.

Your grades on five tests:

95, 87, 92, 100, and 85

Put them in order from least to greatest

85, 87, 92, 95, 100

The middle number is the median

Your median test grade is 92 – half the time you score below 92 and half the time below 92

Your grades on six tests:

95, 87, 92, 100, and 94

Put them in order from least to greatest

85, 87, 92, 94, 95, 100

The middle is between 2 numbers

The median is the mean of 92 and 94

Or

92 + 94 = 186

186 divided by 2 = 93

How do I identify the mode of a set of numbers?

• Arrange the set of numbers in order from least to greatest.

• The number that occurs the most often is the mode of that set of numbers.

ModeThe number in a data set that occurs most often

Your grades: 95, 87, 85, 100, 100

Your mode is 100

Most of the time you get a 100

You don’t have to have a mode…….

Some data sets have no mode or no number that occurs more than others

Some might have two modes

Another way to describe data

Asks the Question:

How spread out is my data?

How is the range of a set of numbers identified?

• Arrange the numbers in the set in order from least to greatest.

• Subtract the lowest number from the highest number in the set of numbers.

• The difference of the two numbers is the range of a set of numbers.

Back to your test Scores:

95, 87, 92, 100, and 94

Your highest score is a 100

Your lowest score is 87

Your range is 100 – 87 = 13

The range = 13

It’s Time To Practice!Number of pets owned by 7 students:

2, 1, 1, 4, 3, 2, 1

What is the mean 2

What is the median 2

What is the Mode 1

What is the Range 3

4 ways to describe dataThe Mean – what we usually think of as the average…..

The Median – The middle number in a data set…..50% of the numbers are above and 50% are below the median

The Mode – The number that occurs most often…..

The Range – the difference between the smallest and bigest number…..