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 (put in L 1 ): Find the mean. Find the deviations (put in L 2 ). What is the sum of the deviations from the mean? 28 0

Square the deviations (put in L 3 ): Find the mean of the squared deviations: Find the sum of the square of the deviations

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

AP Statistics Wednesday, 16 September 2015 OBJECTIVE TSW examine the role of variability in data sets. ASSIGNMENTS DUE –WS Means and Medians  wire basket TODAY’S ASSIGNMENT –WS Mean and Variance  due Friday, 09/15/15 –WS Comparative Box Plots  due Monday, 09/18/15 QUIZ: Means, Medians, Boxplots is on Friday, 18 September 2015.

Calculation of variance of a sample df

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

Calculation of standard deviation

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

Which measure(s) of variability is/are resistant (not affected by outliers)?

Linear transformation rule When multiplying or adding a constant to a random variable, the mean changes by both. When multiplying or adding a constant to a random variable, the standard deviation changes only by multiplication. Formulas:

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

Assignment WS Mean and Variance –Due on Friday, 18 September Next QUIZ: Means, Medians, Variability – Friday, 18 September 2015 Next TEST: Displaying Data – Wednesday, 23 September 2015