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Variability. 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)

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Why is the study of variability important
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
Measures of Variability

range (max-min)

interquartile range (Q3-Q1)

deviations

variance

standard deviation

Lower case Greek letter sigma


Variability

Suppose that we have these data values:

24 34 26 30 37 16 28 21 35 29

Find the mean.

Find the deviations.

What is the sum of the deviations from the mean?


Variability

24 34 26 30 37 16 28 21 35 29

Square the deviations:

Find the average of the squared deviations:


Variability

The average of the deviations squared is called the variance.

parameter

statistic

Population Sample



Variability

Astandard deviation is a measure of the average deviation from the mean.



Degrees of freedom df
Degrees of Freedom (df)

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




Linear transformation rule
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:


Variability

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

If variables are independent 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), ALWAYSadd the variances, then take the square root.

  • Formulas:


Variability

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?