Part IIigma Freud & Descriptive Statistics

Chapter 2

Means to an End:

Computing and Understanding Averages

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

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

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

XX

n

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

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)

Weighted Mean Flying Proficiency Test(Salkind p. 23)

Value Frequency Value*Freq

97 4 388

94 11 1,034

92 12 1,104

91 21 1,911

90 30 2,700

89 12 1,068

78 9 702

60 1 60

Total 100 8967

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

Value Frequency Value*Frequency

5 (ie. False starts, illegal downfield)

4

10 (offensive holding) 4

11 (Half the distance penalties on kickoffs/punts)

3

15 (personal fouls) 2

Total

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?

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

Cumm Percentage of Ages (N=20)Ages freq % Cumm %

15-19 6 .30 .30

20-25 4 .20 .50

26-30 5 .25 .75

31-35 5 .25 1.00

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 = 90Republicans = 70Independents = 140 – the MODE!!

When two values occur the same number of times -- Bimodal distribution

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

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

Chapter 3 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.

Chapter 3 16

Measures of Central TendencyChoosing the right measure

Positively skewed Mean: little high Median: middle score Mode: little low

Median works best

Chapter 3 17

Measures of Central TendencyChoosing the right measure

Negatively skewed Mean: too low Median: middle score Mode: little high

Median works best

Central Tendencies and Distribution Shape

Using SPSS

Glossary Terms to Know Average Measures of Central Tendency

Mean Weighted mean Arithmetic mean

Median Percentile points outliers

Mode