Measures of Central Tendencies

A review of terms and extension

Measures of Central Tendencies Measure of Central

Tendency

Mean

One number that represents a data set and gives an idea of the middle quantity of the data set.

Adding all of the numbers and dividing by how many numbers are in the data set

Measures of Central Tendencies Median

Mode

When the numbers are in order, the middle number. If there are two middle numbers, add them and divide by 2.

The number that shows up most in a data set.

Measures of Central Tendencies Outlier A number that is very

far away from the rest of the data set.

An outlier moves the average from the middle of the cluster of the rest of the data points.

What do we know when given: Mean

Ex. Mean of text messages per day of students is 40

Mean and how many points are in a data set Ex. Mean of text

messages per day of students is 40 and we surveyed 100 students

We know some are more or less than 40, but 40 is the average

We know the above but we also know the total of text messages set by all 100 students 40 * 100 = 4000

What do we know when given: Mean, number in data

set, total of all but one data point Mean=40, 100 students

surveyed, 99 students total 3932

We know same as before, but since we know the total of 100 students is 4000 and the total of the 99 is 3932, we also know the last person texted 4000-3932=68 times.

What do we know when given: Median is 50

Median is 50 and there is an odd number of data points

Median is 50 and Mean is 40

We know half of the data is below 50 and half is above 50

50 is one of the data points in the set

The data set below 50 is further away from 50 than the data set above 50 (see board)

What do we know when given: Median is 50 and

there are 80 data points

Modeex. Mode = 55

We know that 40 data points are below the number 50 and 40 data points are above the number 50.

We know that 55 showed up the most often

When are each useful? Mean

Median

Mode

When we want to know the middle taking into account how big and small the numbers are

When we want to know the middle and there may be an outlier affecting the mean

When we want to know what shows up the most, like in a voting situations,

Measure of Central Tendency Think of specific examples of when you

might use each Pair up with a neighbor and brainstorm if

you are stuck on any Share with the class what your ideas are

Should we try any??