1. Descriptive Statistics
Measures of Central Tendency and Measures of Dispersion

2. Measures of Central Tendency
researchers utilize “averages” to summarize what the data has in common
all three types of averages (mean, median, mode) attempt to define the center point of a distribution.
in a standard normal distribution, all three averages would be exactly in the middle
researchers need to simplify their data, get a “handle” on the numbers, find ways of summarizing the numbers.
measures of central tendency look for similarities in the data, what the numbers have in common

3. the standard normal distribution
In a normal, symmetrical distribution, the mean, median, and mode would all occupy the same position (in the center of the distribution of scores)

4. three measures of central tendency
mean
median
mode

5. Mean the arithmetic average
Think of the mean as the “balance point” of a distribution
example: if you have 10 glasses of water, each with a different amount, and you pour them into a bowl, then redistribute the water in equal amounts, you have the mean (obvious, eh?)
the most sensitive measure of central tendency
affected by extreme scores, or “outliers”: a change in any score affects the mean
μ (mu) refers to the population mean
x̄ (xbar) refers to the sample mean

6. Median
the physical midpoint of a distribution that divides the distribution into two equal halves
the halfway point of a distribution; there are as many scores above the median as below
the median remains unaffected by extreme scores or “outliers.”
typically reported along with the mean in published studies

7. How to find the median:
A set of scores: 98, 86, 46, 63, 66, 94, 31, 56, 51, 75, 48
Step 1: put the scores in order: 31, 46, 48, 51, 56, 63, 66, 75, 86, 94, 98
Step 2: Count off from each end toward the middle*
There are 11 values, so we get 2 groups of 5 with one left over.
31, 46, 48, 51, 56, 63 66, 75, 86, 94, 98
The median is 63
*note: to calculate the median with an even number of scores, take the mean of the two middle scores.

8. Mode the simplest measure of central tendency
only takes some scores into account
the mode is the most common or prevalent score
some distributions are “bimodal” or “multi-modal”
Some distributions have no mode
Marital status
frequency
single 93
Married 86
separated 42
divorced 89
other 20
total
330

9. by themselves, measures of central tendency can be misleading
Example: four married couples complete a “Marital Satisfaction Scale,” rating their happiness on a 1-5 scale (1 = extremely satisfied, 5 = extremely dissatisfied)
Couple A
Wife’s score: 3
Husband’s score: 3
Couple B
Couple C
Wife’s score: 5
Husband’s score: 1
Couple D
Wife’s score: 2
Husband’s score: 4
The means for the four couples are the same (mean = 3). However, we could hardly say the couples are equally satisfied.

10. measures of dispersion
measures of central tendency explain little about how scores differ or vary from one another.
also needed are measures of variability, that is, summary statistics that show how much scores differ, and how far away they are from the center point of a distribution