Chapter 3 Basic Statistics Section 2.2: Measures of Variability

When we are “describing” a group, we usually report one or more measures of central tendency along with one or more measures of variability. When we are “describing” a group, we usually report one or more measures of central tendency along with one or more measures of variability. Variability scores Variability scores Range of scores Range of scores Standard deviation Standard deviation

Measures of Variability Be able to compute and interpret standard deviation Be able to compute and interpret standard deviation Know the computational difference between the standard deviation of a population compared to the standard deviation of a sample. Know the computational difference between the standard deviation of a population compared to the standard deviation of a sample.

Standard Deviation Conceptually it is a measure of how the scores are “spread out” around the mean of the scores Conceptually it is a measure of how the scores are “spread out” around the mean of the scores You can think of standard deviation as the “average difference” (average = standard and difference = deviation) between the scores and the mean You can think of standard deviation as the “average difference” (average = standard and difference = deviation) between the scores and the mean

Standard Deviation There are at least 2 common formulas for standard deviation – one is known as the conceptual formula and one is known as the computational formula There are at least 2 common formulas for standard deviation – one is known as the conceptual formula and one is known as the computational formula The conceptual formula is preferred for understanding standard deviation while the computational formula is easier to use if you are using a calculator The conceptual formula is preferred for understanding standard deviation while the computational formula is easier to use if you are using a calculator

Standard Deviation Conceptual formula (use N for a population but use N-1 for a sample) Conceptual formula (use N for a population but use N-1 for a sample)

Standard Deviation You will notice that the only difference between calculating standard deviation for a population and sample is what you divide by in the formula You will notice that the only difference between calculating standard deviation for a population and sample is what you divide by in the formula Use N for a population Use N for a population Use N-1 for a sample Use N-1 for a sample Consider that the difference will be small when N is very large, but the difference will be large when N is small. Consider that the difference will be small when N is very large, but the difference will be large when N is small.

Standard Deviation The computational version of the formula looks like this: The computational version of the formula looks like this:

Variance Note that the variance is just the standard deviation squared, or… Note that the variance is just the standard deviation squared, or…

A good web site: Var.htm#II4 Var.htm#II4 Var.htm#II4 Var.htm#II4 Take a look at the website above for a great presentation on descriptive statistics (I’m sure there are many more) Take a look at the website above for a great presentation on descriptive statistics (I’m sure there are many more) Note the table of symbols used to represent mean, variance, and standard deviation for samples and populations (about 2/3 down the page) Note the table of symbols used to represent mean, variance, and standard deviation for samples and populations (about 2/3 down the page)