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Variability

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Variability

Allows us to distinguish between usual & unusual values

In some situations, want more/less variability

scores on standardized tests

time bombs

medicine

range (max-min)

interquartile range (Q3-Q1)

deviations

variance

standard deviation

Lower case Greek letter sigma

Suppose that we have these data values:

24342630371628213529

Find the mean.

Find the deviations.

What is the sum of the deviations from the mean?

24342630371628213529

Square the deviations:

Find the average of the squared deviations:

The average of the deviations squared is called the variance.

parameter

statistic

PopulationSample

df

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

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

IQR

- 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?

If variables are independent

- 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:

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?