# Calculating Averages

In accounting, we use averages to represent a set of numbers. Averages allow us to compare two or more different sets of numbers, or to compare an individual with a set of numbers. For example, we could calculate the average exam score for your tutorial class and compare it to other tutorial classes, or compare your individual exam score with the average score in your class.

To calculate an average, we calculate the sum of a list of numbers and divide it by however many numbers are in the list.

For example, assume the group assignment marks in your class were 75, 63, 94 and 79. To calculate the average assignment mark;

Step 1 – Calculate the sum of the list of numbers.
\newcommand{\ctext}{\style{font-family:Arial}{\text{#1}}} \begin{align*}\ctext{Sum of list} &= 75 + 63 + 95 + 79 \cr &= 312 \end{align*}
Step 2 – Divide the sum by the number of values in the list.
\begin{align*} \ctext{Average} &= \frac{312}{4} \cr &= 78 \end{align*}
The average group assignment mark for the class was 78. If your group scored less than 78, it would be a below average score. If you scored more than 78, your group would be performing above the average.

In an accounting problem, we might use averages to find a figure such as the average profit over the past three years. Given that profit has been recorded as \$130,000, \$145,750 and \127,500, the average would be calculated as; \begin{align*} \ctext{Average} &= \frac{\left(130,000 + 145,750 + 127,500\right)}{3} \cr &= \134,417 \end{align*} The average profit for the three year period was \134,417.