Part II S igma Freud & Descriptive Statistics

1. Part IISigma 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 and weighted mean for a set of scores • Computing the mode using the mode and the median for a set of • 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 “Measure 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 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. Weighted Mean Flying Proficiency Test(Salkind p. 23)

8. You Try!! Using Weighted Mean to Find Average Super Bowl Yardage Penalty

9. Computing the Median • Median = point/score at which 50% of remaining scores fall above and 50% fall below. • 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?

10. 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

11. Cumm Percentage of Ages (N=20)

12. 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

13. Using Calculator • Mode + . = statistical mode; • Shift +7= the mean “x-bar” • Shift +5= sum of x; square this value to get square of the sum; • Shift +4 = sum of squares • Shift +9= sample standard deviation • Shift+1=permutations • Shift+2=combinations • Shift+3= factorials

14. When to Use What… • Use the Mode • 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

15. Measures of Central TendencyChoosing the right measure • Normal distribution • Mean: = median/mode • Median: = mean/mode • Mode: = mean/median • They all work. • Pick the one that fits the need.

16. Measures of Central TendencyChoosing the right measure • Positively skewed • Mean: little high • Median: middle score • Mode: little low • Median works best

17. Measures of Central TendencyChoosing the right measure • Negatively skewed • Mean: too low • Median: middle score • Mode: little high • Median works best

18. Central Tendencies and Distribution Shape

19. Using SPSS

20. Glossary Terms to Know • Average • Measures of Central Tendency • Mean • Weighted mean • Arithmetic mean • Median • Percentile points • outliers • Mode