DO NOW: On your DO NOW sheet in the Tuesday box: What is a common diagram psychologists use to describe data? Why can this graph be misleading?

Central Tendency, Variation, and Generalization AP Psychology Ms. Desgrosellier

Objectives: SWBAT describe three measures of central tendency, and tell which is most affected by extreme scores. SWBAT describe two measures of variation. SWBAT identify three principles for making generalizations from samples.

Measures of Central Tendency Mode: the most frequently occurring score or scores Organize data in order, by grouping the same number together Example: Find the mode: 5, 3, 4, 5, 7, 5, 1, 9, 5

Measures of Central Tendency Mean: the most commonly reported measure, also known as the arithmetic average Total up the scores and divide by the total number of scores Example: Find the mean: 5, 2, 9, 6, 3, 5

Measures of Central Tendency Median: the midpoint, or the 50th percentile The middle score; half the points are above it and half are below it Arrange the scores from highest to lowest and the median number is the one in the middle If you have an even number of data points, you should find the mean of the two middle scores Example: find the median: 8, 3, 5, 7, 1, 3, 6

Skewed Data

The mean is greatly affected by extreme scores Remember: always note which measure of central tendency is reported. Then, if it is a mean, consider whether or not a few atypical scores could be distorting it.

Measures of Variation Variation of data: how similar or diverse the scores are. Averages from data with low variability are more reliable than averages based on scores with high variability E.g. Soccer player who scores 2-4 goals a game. We would by more confident saying he would score 3 goals a game than if his goal count varied from 0 – 10

Measures of Variation Range: the gap between the lowest and highest scores Only provides a rough estimate of variation because a couple of extreme scores will create a deceptively large range

Measures of Variation Find the range of this data set: Chris took 7 math tests in one quarter. What is the range of his test scores? 89, 73, 84, 91, 87, 77, 94 Ordering the test scores from least to greatest, we get: 73, 77, 84, 87, 89, 91, 94 highest - lowest = = 21 Answer: The range of these test scores is 21 points.

Measures of Variation Standard deviation: a computed measure of how much scores vary around the mean score A better gauge of how scores are spread out because it uses information from each score

Measures of Variation

Making Inferences Data are “noisy” Average scores could vary because of random fluctuation or chance in the sample How can we infer that an observed difference accurately estimates the true difference?

Three Principles: 1. Representative samples are better than biased samples Remember to keep in mind what population a study has sampled All men or all women? One education or income level? All young or all older? Etc.

Three Principles: 2. Less-variable observations are more reliable than those that are more variable An average is more reliable when it comes from scores with low variability Why? Extreme scores greatly affect the average!

Three Principles: 3. More cases are better than fewer Averages based on many cases are more reliable (less variable) than averages based on only a few cases. E.g. If you visit two colleges and find two professors at one school are better than two at the other, you could say that the first university is clearly better. However, you only met two of the hundred faculty members.

Three Principles: Remember: don’t be overly impressed by a few stories. Generalizability based on a few unrepresentative cases is unreliable.