# Unit 10 Statistics 6SP 1,2,3

## Essential Question Choices:

1. What do the measures of center (mean and median) reveal about real world data?

2. Why is data collected?

3. Why is variability important in statistics?

## Vocabulary Words to know!

Statistical question, data, variability, center, mean (average), median, mode, range, spread, measure of center, measure of variation, frequency, outliers

## What is a Measure of Variability?

Measures of variability tell us how spread out the scores in a distribution are.

EX: Suppose you got a 75 out of 100 on a math test, and you know that the mean score in the class was 65. Now you know you've done better than average, so that's a good thing, but you don't know how much better than average you have done. For example, if most people scored at or near the mean, then your score may actually be quite high in comparison to all of the others.

On the other hand, if the scores were quite spread out, then your score may be little better than average.

A. Concept of variability

A distribution of scores has high variability if the scores are widely distributed around a mean. A distribution of scores has low variability if most of the scores lie fairly close to the mean. From the test example above, with an average of 65: a distribution with high variability would include scores like 15, 98, 72, 27, 4, etc. A distribution with low variability would include scores like 66, 62, 67, 64, etc.

B. Range

The range of a distribution is defined as the largest score minus the lowest score. For example, in the distribution (2, 9, 5, 7, 4, 3), the range would be 9 - 2 = 7. As you can see, the range only takes into consideration 2 numbers: the highest and the lowest. For this reason, it is a rather rough measure of variability.

• What is Distribution? an arrangement of values of a variable showing their frequency of occurrence

sources: http://www.lmc.edu/Faculty/carson/Stats/ST02CentTendVar.html