3.2 measures of variability
DESCRIPTION
3.2 Measures of Variability. Objectives: By the end of this section, I will be able to… Understand and calculate the range of a data set. Explain in my own words what a deviation is. Calculate the variance and the standard deviation for a population or a sample. What is variation ?. - PowerPoint PPT PresentationTRANSCRIPT
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.