2.4 Measures of Variation2.4 Measures of Variation

Coach BridgesCoach Bridges

NOTESNOTES

What you should learn….What you should learn….

How to find the range of a data setHow to find the range of a data set How to find the variance and standard How to find the variance and standard

deviation of a population and of a sampledeviation of a population and of a sample How to use the Empirical Rule to interpret How to use the Empirical Rule to interpret

standard deviationstandard deviation

Measures of VariationMeasures of Variation

Range - Range - Data set is the difference between Data set is the difference between the maximum and minimum data entries in the maximum and minimum data entries in the setthe set – Range= (Max) – (Min)Range= (Max) – (Min)

DeviationDeviation

Deviation - Deviation - An entry x in a population data An entry x in a population data set is the difference between the entry and set is the difference between the entry and the mean of the data setthe mean of the data set– Deviation of x= x – meanDeviation of x= x – mean

Guidelines for Finding Population Guidelines for Finding Population

Variance and Standard DeviationVariance and Standard Deviation

1.1. Find the mean of the population data set.Find the mean of the population data set.

2.2. Find the deviation of each entryFind the deviation of each entry

3.3. Square each deviationSquare each deviation

4.4. Add to get the sum of squaresAdd to get the sum of squares

Guidelines for Finding Population Guidelines for Finding Population Variance and Standard DeviationVariance and Standard Deviation

5. 5. Divide by N to get the population Divide by N to get the population variancevariance

6.6. Find the square root of the variance to Find the square root of the variance to get the population standard deviation.get the population standard deviation.

Guidelines for Finding the Sample Guidelines for Finding the Sample

Variance and Standard DeviationVariance and Standard Deviation

1.1. Find the mean of the sample data set.Find the mean of the sample data set.

2.2. Find the deviation of each entryFind the deviation of each entry

3.3. Square each deviationSquare each deviation

4.4. Add to get the sum of squaresAdd to get the sum of squares

5.5. Divide by n – 1 to get the sample varianceDivide by n – 1 to get the sample variance

6.6. Find the square root of the variance to get Find the square root of the variance to get the sample standard deviationthe sample standard deviation

Empirical Rule (Or 68-95-99.7 Empirical Rule (Or 68-95-99.7 Rule)Rule)

For data with a (symmetric) bell-shaped For data with a (symmetric) bell-shaped distribution, the standard deviation has the distribution, the standard deviation has the following characteristics:following characteristics:

1.1. About 68% of data lies within one standard About 68% of data lies within one standard deviation of the meandeviation of the mean

2.2. About 95% of data lies within two standard About 95% of data lies within two standard deviations of the meandeviations of the mean

3.3. About 99.7% of data lies within three About 99.7% of data lies within three standard deviations of the meanstandard deviations of the mean