This chapter covers the concept of averages and how to calculate the average of a given set of data.

EO 1.3Given a set of numbers, CALCULATE the average value.

An average is the sum of a group of numbers or quantities divided by the number of numbers or quantities. Averages are helpful when summarizing or generalizing a condition resulting from different conditions. For example, when analyzing reactor power level, it may be helpful to use the average power for a day, a week, or a month. The average can be used as a generalization of the reactor power for the day, week, or month.

Average calculations involve the following steps:

Step 1: Add the individual numbers or quantities. Step 2: Count the number of numbers or quantities. Step 3: Divide the sum in Step 1 by the number in Step 2.

Example 1:

Find the average cost of a car, given the following list of prices. $10,200; $11,300; $9,900; $12,000; $18,000; $7,600

Solution:

Step 1: 10200 + 11300 + 9900 + 12000 + 18000 + 7600 = 69000 Step 2:

Total number of prices is 6

Step 3: Divide 69000 by 6. The result is 11500

Thus, the average price of the six cars is $11,500.

Example 2:

Find the average temperature if the following values were recorded: 600F, 596F, 597F, 603F

Solution:

Step 1: 600 + 596 + 597 + 603 = 2396

Step 2: The number of items is 4.

Step 3: 2396/4 = 599F

Average Value

The summation symbol, , introduced in the first chapter, is often used when dealing with the average value, .

Using the first example in this chapter, the average value could have been expressed in the following manner:

where:

The right side of the above equation can then be rewritten.

substituting 10,200 for x_l, 11300 for x₂, 9,900 for x₃, etc.

Example:

If we were to apply the average value equation from above to the second example concerning temperature, how would it be written, and what would be the values for N₁, x_i?

Solution:

Summary

The important information from this chapter is summarized below.

Averages Summary

Calculating the average of a set of numbers requires three steps:

1. Add the individual numbers or quantities.

2. Count the number of numbers or quantities added in previous step.

3. Divide the sum calculated in step 1 by the number in step 2.