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

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2 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

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

4 Suppose that we have these data values: 2434263037 1628213529 Find the mean. Find the deviations. What is the sum of the deviations from the mean?

5 2434263037 1628213529 Square the deviations: Find the average of the squared deviations:

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

7 Calculation of variance of a sample df

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

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

10 Calculation of standard deviation

11 Use calculator

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

13 Activity

14 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.

15 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?

16 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

17 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 Unpacking3.50.7 Assembly21.82.4 Tuning12.32.7

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