Calculating Averages

Calculating Averages

Introduction

There are many instances when it is important to know the average (mean) value of a set of numbers. In sports we are interested in one’s bowling average or batting average. In supply management we may want to know average demand for an item for a given time period, e.g., a month. We may also want to know the average demand for the entire year. Here is how to calculate these averages.

	The Professor Says: To calculate an average, follow these three steps:
	Step 1. Step 2. Step 3.	Add (total) all of the numbers in the set you want to average. Count how many numbers are in the set. Divide the total (sum) from step 1 by the result of your count from step 2.

Example

Calculate the average of the following set of numbers:
      126, 134, 155, 101, 144, 138, 151, 139
       Step 1. 126 + 134 + 155 + 101 + 144 + 138 + 151 + 139
                     = 1,088

       Step 2. There are 8 numbers in the set.

       Step 3. 1,088 8 = 136

	The Professor Says: When calculating the average over several time periods, do not average the average values for the time period! You must take the average of all of the values in all of the time periods, following these steps.
	Step 1. Step 2. Step 3.	Find the total of all of the numbers in all of the sets you want to average. Determine the total number of numbers in all of the sets. Divide the total from Step 1 by the total number from Step 2.

    Example

Given the following demand history information with the calculations of the averages for each quarter as follows:

1^st Qtr.

2^nd Qtr.

3^rd Qtr.

4^th Qtr.

Tot 4 Qtrs

TOTAL
2,462

657

970

839

4,928

FREQ.
237

101

149

128

615

Item Manager’s Calculation

Averages
10.39

6.50

6.51

6.55

8.01

Calculate the average for the year.

Step 1.    2,462 + 657 + 970 + 839 = 4,928
Step 2.    There are 615 total numbers in the set.

Step 3.    The average of the averages is 8.01

Note:       If you add the quarterly averages (10.39 + 6.50 + 6.51 + 6.55 =
               29.95) and divide by 4 (= 7.49), you get an answer that is
               different from the average for the year.


Practice