1. …an open, online course
Statistics in Education for Mere Mortals Descriptive Statistics: The Standard Deviation
Lloyd P. Rieber
Professor of Learning, Design, & Technology
The University of Georgia
© 2013 Lloyd P. Rieber

2. Ted Williams was the Last .400 Hitter in Major League Baseball
Why?
Interesting statistic:
The overall major league batting average has always been around .260.
© 2013 Lloyd P. Rieber

3. © 2013 Lloyd P. Rieber

4. So, Which Is It?
Are you interested in collecting data on a population?
Are you interested in knowing about a population, but can only collect data on a sample?
Or, are you interested in collecting data on a sample, but don’t care about the population?
The statistics you actually compute will differ depending on your answer.
© 2013 Lloyd P. Rieber

5. Start Here Population Incomplete Sample sampling description
inference
Parameter
Statistic
© 2013 Lloyd P. Rieber

6. Surveying a Population: the United States Census
© 2013 Lloyd P. Rieber

7. Excerpts From Ruling on Planned Use of Statistical Sampling in 2000 Census
Reading section 141(a) and section 195 together, and considering the plain text, legislative history and other tools of statutory construction, this court finds that the use of statistical sampling to determine the population for purposes of the apportionment of representatives in Congress among the states violates the Census Act
© 2013 Lloyd P. Rieber

8. Dealing with Mathematical Symbols
5 + 5 = 10
10 ÷ 2 = 5
10 / 2 = 5
7 X 3 = 21
7 * 3 = 21
7  3 = 21
© 2013 Lloyd P. Rieber

9. Dealing with Mathematical Symbols
Compare the statement…
“Compute the mean for a set of numbers.”
to...
____
Population
µ =
∑ X N
Sample
X =
∑ X N
____ __
© 2013 Lloyd P. Rieber

10. Two Important Types of Descriptive Statistics
Measures of Central Tendency
Measures of Variability
Kurtosis…
The curve’s quality
of “peakedness”
© 2013 Lloyd P. Rieber

11. How to measure variability?
Method 1: Compute the difference between the highest and lowest score
OK, but this only takes into account 2 scores!
Method 2:
Method 3:
© 2013 Lloyd P. Rieber

12. How to measure variability?
Method 1: Compute the difference between the highest and lowest score
OK, but this only takes into account 2 scores!
Method 2: Compute the difference between each score and grand mean (aka group ave.)
OK, these are called deviation scores.
Great! Let’s take the average of them.
Oops! The answer is always 0!
Method 3
© 2013 Lloyd P. Rieber

13. How to measure variability?
Method 1: Compute the difference between the highest and lowest score
OK, but this only takes into account 2 scores!
Method 2: Compute the difference between each score and group average
OK, these are called deviation scores.
Great! Let’s take the average of them.
Oops! The answer is always 0!
Method 3: Compute the standard deviation
Square the difference scores first, then take the square root. Pretty clever! Consider it as an average of how much each score varies from the group.
© 2013 Lloyd P. Rieber

14. Standard Deviation When Describing a Sample
© 2013 Lloyd P. Rieber

15. Standard Deviation Estimating the Population Parameter from a Sample
Ŝ =
© 2013 Lloyd P. Rieber

16. Girl Scout Cookie Sales
Boxes of Cookies
Deviation Scores X x2 28 18
324 11 1 10 5 -5 25 4 -6 36 2 -8 64
∑X=60
∑x=0
∑x2=450
Example taken from Spatz, 1997.
© 2013 Lloyd P. Rieber

17. © 2013 Lloyd P. Rieber

18. Ted Williams was the Last .400 Hitter in Major League Baseball
Why? The answer may involve the principle of variance.
The major league batting average has always been around .260, but…
© 2013 Lloyd P. Rieber

19. …an open, online course
Statistics in Education for Mere Mortals Descriptive Statistics: The Standard Deviation
Lloyd P. Rieber
Professor of Learning, Design, & Technology
The University of Georgia
© 2013 Lloyd P. Rieber