3.2 Measures of Variability

Objectives:By the end of this section, I will beable to…

1) Understand and calculate the range of a data set.

2) Explain in my own words what a deviation is.

3) Calculate the variance and the standard deviation for a population or a sample.

What is variation?

It is the spread of the

numbers around the

mean.

Measures of Variation

1. Variance

2. Standard Deviation

3. Range

22 ( )

1

x xs s

n

22 ( )

1

x xs

n

Highest – Lowest

Why is VARIATION important?

Because less variation means smaller

spread in the data, which means

1. More precise estimates

2. Higher confidence in our

conclusions about the data

Wall Street Journal competition

Stocks were chosen by1. Journal staff randomly throwing darts

at a list of the stocks2. A team of four financial experts3. The DJIA (Dow Jones Industrial

Average)

THE RESULTS ARE…

Variations and Graphs

Measuring V-Span

1. Make a V between your index finger and your middle finger when you spread them as far as possible.

2. Measure to the nearest tenth of a centimeter.

Your V-Span =

3. Compute the group’s mean V-Span.

Mean V-Span =

4. Now fill out the following chart with your data and find the three values of variation

x x-mean (x-mean)2

Variance =

Sum/(n – 1)

Put in all of your V-spans as x values. Add rows as necessary.

Then use the mean (average V-span) and find the difference between each x value and the mean

Square the number you just found…

Standard deviation = Square ROOT of the variance

Calculator Time

Find the variance and standard deviation on your calculator.

NASCAR TIME - link

On a separate sheet of paper, and one per person – NEATLY complete the following.

Find the mean, median, mode, range, variance, and standard deviation of NASCAR points of the top 10 drivers for 2010.