S ECTION 3.3 Measures of Variation

A NOTHER N EW M EASURE - V ARIANCE OF A S AMPLE 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: $ s²=3,712,571.7 dollars² s = $ Damage of $10,000 is not unusual because it is within 2 standard deviations from the mean.

8. Range: s²= s = 58.3 A FICO score 500 is unusual because it is more than 2 standard deviations below the mean.

9. Range: $29.6 million s²=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.

S TANDARD D EVIATION MADE EASY ! Hit 2 nd 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.

R EAL L IFE A PPLICATION – C USTOMER W AITING T IMES Do you prefer single waiting lines or multiple wait lines?

R EAL L IFE A PPLICATION – C USTOMER W AITING T IMES 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 Providence

M INI -A CTIVITY 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.

A PPLICATION Would any of the characters of Eclipse have an “unusual” height in our class?

A DDITIONAL P RACTICE Pg. 111 # 14-16