690+measures+of+central+tendency

Measures of central tendency

from Marcie's study session

3 types of measures of cent. tendency: looking at centrality, heavily influenced by outliers
 * mean**: arithmetic average, its exact bc its a calculation, but influence by many factors like outliers
 * median**: midpoint (more stable, same # of cases above than below) must have real #'s rather than ratings, bc not enough variance
 * mode**: most frequently recurring score
 * range:** difference betw. highest and lowest scores, showing variability

The Standard Deviation
The standard deviation is a very common method used in science to describe the variability in a set of numbers. It examines the spread (variability) of each data point around the mean. The standard deviation increases with an increase in the variability of the data. If every score in the data set are the same, then the standard deviation will equal zero.

Standard Deviation

The **standard deviation** is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation.

Why is this useful? Here's an example: If you are comparing test scores for different schools, the standard deviation will tell you how diverse the test scores are for each school. Let's say Springfield Elementary has a higher mean test score than Shelbyville Elementary. Your first reaction might be to say that the kids at Springfield are smarter. But a bigger standard deviation for one school tells you that there are relatively more kids at that school scoring toward one extreme or the other. By asking a few follow-up questions you might find that, say, Springfield's mean was skewed up because the school district sends all of the gifted education kids to Springfield. Or that Shelbyville's scores were dragged down because students who recently have been "mainstreamed" from special education classes have all been sent to Shelbyville. In this way, looking at the standard deviation can help point you in the right direction when asking why information is the way it is. The standard deviation can also help you evaluate the worth of all those so-called "studies" that seem to be released to the press everyday. A large standard deviation in a study that claims to show a relationship between eating Twinkies and killing politicians, for example, might tip you off that the study's claims aren't all that trustworthy.