Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability –scores.

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Presentation transcript:

Why is the study of variability important? Allows us to distinguish between usual & unusual values In some situations, want more/less variability –scores on standardized tests –time bombs –medicine

Measures of Variability range (max-min) interquartile range (Q3-Q1) deviations variance standard deviation Lower case Greek letter sigma

Suppose that we have these data values: Find the mean. Find the deviations. What is the sum of the deviations from the mean?

Square the deviations: Find the average of the squared deviations:

The average of the deviations squared is called the variance. PopulationSample parameter statistic

Calculation of variance of a sample df

Degrees of Freedom (df) n deviations contain (n - 1) independent pieces of information about variability

A standard deviation is a measure of the average deviation from the mean.

Calculation of standard deviation

Use calculator

Which measure(s) of variability is/are resistant?

Activity

Linear transformation rule When adding a constant to a random variable, the mean changes but not the standard deviation. When multiplying a constant to a random variable, the mean and the standard deviation changes.

An appliance repair shop charges a $30 service call to go to a home for a repair. It also charges $25 per hour for labor. From past history, the average length of repairs is 1 hour 15 minutes (1.25 hours) with standard deviation of 20 minutes (1/3 hour). Including the charge for the service call, what is the mean and standard deviation for the charges for labor?

Rules for Combining two variables To find the mean for the sum (or difference), add (or subtract) the two means To find the standard deviation of the sum (or differences), ALWAYS add the variances, then take the square root. Formulas: If variables are independent

Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the times for each setup phase are independent with the following means & standard deviations (in minutes). What are the mean and standard deviation for the total bicycle setup times? PhaseMeanSD Unpacking Assembly Tuning