The Mathematics of Money

A. Measures of Variation

1. Suppose that a company is testing the durability of its light bulbs. The company tests fi ve bulbs to see how long they will
   last and fi nds that the hours each bulb lasts are: 835, 842, 808, 798 and 907.

a. Calculate the mean number of hours these bulbs lasted.

b. Complete the table below:

Hours Deviation Deviation Squared

835

842

808

798

907

Total

c. Use the values you calculated in the table for part b to calculate the standard deviation of the hours the bulbs

lasted.

2. Suppose that a bakery is testing how consistent the weights of its bread loaves are. The company tests six loaves and
   measures their weights. The weights are 681.3 g, 682.2 g, 685.1g, 680.0 g, 680.0 g, and 679.2 g.

a. Calculate the mean weight of the bread loaves.

b. Complete the table below:

Weight Deviation Deviation Squared

Total

c. Use the values you calculated in the table for part b to calculate the standard deviation of the bread loaves’

weights.

Exercises 16.3 631

EXERCISES 16.3

Our two tools for interpreting standard deviation are summarized in the table below:

Percentage of the Data that Falls

within:

If the Data is Distributed:

Normally (Bell Curve) Any Way at All

1 standard deviation of the mean Approximately 68% Can’t say anything

2 standard deviations of the mean Approximately 95% At least 75%

3 standard deviations of the mean Approximately 99% At least 88.9%

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