chapter 3 basic statistics section 2.2: measures of variability
TRANSCRIPT
Chapter 3 Basic StatisticsChapter 3 Basic Statistics
Section 2.2:Section 2.2:
Measures of VariabilityMeasures of Variability
Measures of VariabilityMeasures of Variability
When we are “describing” a group, we When we are “describing” a group, we usually report one or more measures of usually report one or more measures of central tendency along with one or more central tendency along with one or more measures of variability.measures of variability.
Variability scoresVariability scoresRange of scores Range of scores Standard deviationStandard deviation
Measures of VariabilityMeasures of Variability
Be able to compute and interpret standard Be able to compute and interpret standard deviationdeviation
Know the computational difference Know the computational difference between the standard deviation of a between the standard deviation of a population compared to the standard population compared to the standard deviation of a sample.deviation of a sample.
Standard DeviationStandard Deviation
Conceptually it is a measure of how the Conceptually it is a measure of how the scores are “spread out” around the mean scores are “spread out” around the mean of the scoresof the scores
You can think of standard deviation as the You can think of standard deviation as the “average difference” (average = standard “average difference” (average = standard and difference = deviation) between the and difference = deviation) between the scores and the meanscores and the mean
Standard DeviationStandard Deviation
There are at least 2 common formulas for There are at least 2 common formulas for standard deviation – one is known as the standard deviation – one is known as the conceptual formula and one is known as conceptual formula and one is known as the computational formulathe computational formula
The conceptual formula is preferred for The conceptual formula is preferred for understanding standard deviation while understanding standard deviation while the computational formula is easier to use the computational formula is easier to use if you are using a calculatorif you are using a calculator
Standard DeviationStandard Deviation
Conceptual formula (use N for a Conceptual formula (use N for a population but use N-1 for a sample)population but use N-1 for a sample)
Standard DeviationStandard Deviation
You will notice that the only difference You will notice that the only difference between calculating standard deviation for between calculating standard deviation for a population and sample is what you a population and sample is what you divide by in the formuladivide by in the formulaUse N for a populationUse N for a populationUse N-1 for a sampleUse N-1 for a sample
Consider that the difference will be small Consider that the difference will be small when N is very large, but the difference when N is very large, but the difference will be large when N is small.will be large when N is small.
Standard DeviationStandard Deviation
The computational version of the formula The computational version of the formula looks like this:looks like this:
VarianceVariance
Note that the variance is just the standard Note that the variance is just the standard deviation squared, or…deviation squared, or…
A good web site:A good web site:
http://www.uwsp.edu/psych/stat/5/CT-Var.http://www.uwsp.edu/psych/stat/5/CT-Var.htm#II4htm#II4
Take a look at the website above for a Take a look at the website above for a great presentation on descriptive statistics great presentation on descriptive statistics (I’m sure there are many more)(I’m sure there are many more)
Note the table of symbols used to Note the table of symbols used to represent mean, variance, and standard represent mean, variance, and standard deviation for samples and populations deviation for samples and populations (about 2/3 down the page)(about 2/3 down the page)