SECTION 3.3Measures of Variation

ANOTHER NEW MEASURE - VARIANCE OF A SAMPLE

Definition

The variance of a set of values is a measure of variation equal to the square of the standard

deviation.

Sample variance

7.Range: $4774.0s²=3,712,571.7 dollars² s = $1926.8

Damage of $10,000 is not unusual because it is within 2 standard deviations from the mean.

8.Range: 172.0 s²=3397.0 s = 58.3

A FICO score 500 is unusual because it is more than 2 standard deviations below the mean.

9.Range: $29.6 millions²=148.1million dollars² s = $12.2 million Because the sample values are the 10 highest, they give us almost no information about the variance of the salaries of TV shows in general.

STANDARD DEVIATION MADE EASY! Hit 2nd and click on 0 Select LN Scroll down to “stdDev( ” Hit Enter. Use curly brackets to list your data values ex: stdDev({1,1,1,4,7,7,7}) Hit enter.

OR….

The Range Rule of Thumb

The vast majority (such as 95%) of sample values lie within two standard deviations of the

mean.

REAL LIFE APPLICATION – CUSTOMER WAITING TIMES

Do you prefer single waiting lines or multiple wait lines?

REAL LIFE APPLICATION – CUSTOMER WAITING TIMES

Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all

customers enter a single waiting line) and the Bank of Providence (where all customers wait in individual lines at three different teller

windows) are listed below. Determine whether there is a difference between the

two data sets. Jefferson Valley 6.

56.6 6.

76.8

7.1

7.3

7.4

7.7

7.7

7.7

Providence 4.2

5.4 5.8

6.2

6.7

7.7

7.7

8.5

9.3

10

MINI-ACTIVITY

Write your height in inches up on the side of the board. Once everyone’s height is on the board, use your calculator to calculate the standard deviation of our class’ heights.

APPLICATION Would any of the characters of Eclipse have an

“unusual” height in our class?

ADDITIONAL PRACTICE

Pg. 111 # 14-16