1. Part II Sigma Freud & Descriptive Statistics
Chapter 2    
Means to an End:
Computing and Understanding Averages

2. What you will learn in Chapter 2
Measures of central tendency
Computing the mean for a set of scores
Computing the mode and median
Selecting a measure of central tendency

3. Measures of Central Tendency
The AVERAGE is a single score that best represents a set of scores
Averages are also know as “Measures of Central Tendency”
Three different ways to describe the distribution of a set of scores…
Mean – typical average score
Median – middle score
Mode – most common score

4. Computing the Mean Formula for computing the mean
“X bar” is the mean value of the group of scores
“” (sigma) tells you to add together whatever follows it
X is each individual score in the group
The n is the sample size

5. Things to remember… N = population n = sample
Sample mean is the measure of central tendency that best represents the population mean
Mean is VERY sensitive to extreme scores that can “skew” or distort findings
Average means the one measure that best represents a set of scores
Different types of averages
Type of average used depends on the data and question

6. Weighted Mean Example
List all values for which the mean is being calculated (list them only once)
List the frequency (number of times) that value appears
Multiply the value by the frequency
Sum all Value x Frequency
Divide by the total Frequency (total n size)

7. Computing the Median
Median = point/score at which 50% of remaining scores fall below and 50% fall above.
NO standard formula
Rank order scores from highest to lowest or lowest to highest
Find the “middle” score
BUT…
What if there are two middle scores?
What if the two middle scores are the same?

8. A little about Percentiles…
Percentile points are used to define the percent of cases equal to and below a certain point on a distribution
75th %tile – means that the score received is at or above 75 % of all other scores in the distribution
“Norm referenced” measure
allows you to make comparisons

9. Computing the Mode Mode = most frequently occurring score NO formula
List all values in the distribution
Tally the number of times each value occurs
The value occurring the most is the mode
Democrats = 90
Republicans = 70
Independents = 140: the MODE!!
When two values occur the same number of times -- Bimodal distribution

10. When to Use What… Use the Mode Use the Median Use the Mean
when the data are categorical
Use the Median
when you have extreme scores
Use the Mean
when you have data that do not include extreme scores and are not categorical

11. Using SPSS

12. Glossary Terms to Know Average Measures of Central Tendency Mean
Weighted mean
Arithmetic mean
Median
Percentile points
Outliers
Mode

13. Part II Sigma Freud & Descriptive Statistics
Chapter 3    
Viva La Difference: Understanding Variability

14. What you will learn in Chapter 3
Variability is valuable as a descriptive tool
Difference between variance & standard deviation
How to compute:
Range
Standard Deviation
Variance

15. Why Variability is Important
How different scores are from one particular score
Spread
Dispersion
What is the “score” of interest here?
Ah ha!! It’s the MEAN!!
So…variability is really a measure of how each score in a group of scores differs from the mean of that set of scores.

16. Measures of Variability
Three types of variability that examine the amount of spread or dispersion in a group of scores…
Range
Standard Deviation
Variance
Typically report the average and the variability together to describe a distribution.

17. Computing the Range
Range is the most “general” estimate of variability…
Two types…
Exclusive Range
R = h - l
Inclusive Range
R = h – l + 1
(Note: R is the range, h is the highest score, l is the lowest score)

18. Computing Standard Deviation
Standard Deviation (SD) is the most frequently reported measure of variability
SD = average amount of variability in a set of scores
What do these symbols represent?

19. Why n – 1?
The standard deviation is intended to be an estimate of the POPULATION standard deviation…
We want it to be an “unbiased estimate”
Subtracting 1 from n artificially inflates the SD…making it larger
In other words…we want to be “conservative” in our estimate of the population

20. Things to Remember…
Standard deviation is computed as the average distance from the mean
The larger the standard deviation the greater the variability
Like the mean…standard deviation is sensitive to extreme scores
If s = 0, then there is no variability among scores…they must all be the same value.

21. Computing Variance Variance = standard deviation squared
So…what do these symbols represent? Does the formula look familiar?

22. Standard Deviation or Variance
While the formulas are quite similar…the two are also quite different.
Standard deviation is stated in original units
Variance is stated in units that are squared
Which do you think is easier to interpret???

23. Using the Computer to Compute Measures of Variability

24. Glossary Terms to Know Variability Range Standard deviation Variance
Mean deviation
Unbiased estimate
Variance

25. Part II Sigma Freud & Descriptive Statistics
Chapter 4    
A Picture is Really Worth a Thousand Words

26. What you will learn in Chapter 4
Why pictures are worth “a thousand words”
How to create:
Histogram
Polygon
Other charts/graphs
Using SPSS to create & modify charts
Different types of charts and their uses

27. Why Illustrate Data?
When describing a set of scores you will want to use two things…
One score for describing the group of data
Measure of Central Tendency
Measure of how diverse or different the scores are from one another
Measure of Variability
However, a visual representation of these two measures is much more effective when examining distributions.

28. Ten Ways to a Great Figure
Minimize the “junk”
Plan before you start creating
Say what you mean…mean what you say
Label everything
Communicate ONE idea
Keep things balanced
Maintain the scale in the graph
Remember…simple is best
Limit the number of words
The chart alone should convey what you want to say

29. Frequency Distributions
Method of tallying, and representing the number of times a certain score occurs
Group scores into interval classes/ranges
Creating class intervals
Range of 2, 5, 10, or 20 data points
10-20 data points cover the entire range of data
Largest interval goes at the top

30. Histograms
Class Intervals
Along the x-Axis

31. Histograms
Hand Drawn
Histogram

32. Histogram
Tally-Ho
Method

33. Frequency Polygon
A “continuous line that represents the frequencies of scores within a class interval”

34. Cumulative Frequency Distribution

35. Fat & Skinny of Frequency Distributions
Distributions can be different in four different ways…
Average value
Variability
Skewness
Kurtosis

36. Average Value

37. Variability

38. Skewness
Positive & Negative Skewness

39. Kurtosis
Platykurtic & Leptokurtic

40. Cool Ways to Chart Data
Column Chart

41. Cool Ways to Chart Data
Line Chart

42. Cool Ways to Chart Data
Pie Chart

43. Using the Computer to Illustrate Data
Creating Histogram Graphs

44. Using the Computer to Illustrate Data
Creating Bar Graphs

45. Using the Computer to Illustrate Data
Creating Line Graphs

46. Using the Computer to Illustrate Data
Creating Pie Graphs

47. Glossary Terms to Know Frequency distribution Class interval Histogram
Frequency Polygon
Cumulative Frequency Distribution
Ogive
Skewness
Kurtosis
Platykurtic
Leptokurtic