What it means
Almost every business report contains an average, and the mean is the one most people mean when they say the word. If five months of sales total $240,000, the mean monthly sales figure is $48,000.
It is simple to calculate and easy to explain, which is why it is used in budgets, forecasts and performance reports. The mean is useful because it uses every number in the set.
This makes it suitable for tasks such as working out an average cost, an average price or a typical order size. It is also the starting point for many other measures, including variance and standard deviation, which describe how widely numbers are spread around the mean.
The major weakness is sensitivity to extreme values, known as outliers. If one month has an exceptional one-off sale, the mean rises sharply even though normal trading has not changed.
In such cases, the median (the middle value when numbers are put in order) gives a better picture of what is typical. There are also different kinds of mean.
A weighted mean gives more importance to some values, as when calculating average cost per unit across purchases of different sizes. A geometric mean is used for growth rates and returns over several periods, because it reflects compounding.
Before relying on an average, it helps to ask how many numbers sit behind it and how spread out they are. A mean of $48,000 could come from five months all near $48,000 or from a few huge months and many weak ones, and the decision you make may differ.
In finance, the mean appears in many forms, including average selling price, average cost per unit, average balance and average days to collect payment. Each of these has the same weakness, which is that it hides the spread of the underlying numbers.
A good habit is to show the mean together with the median, or the highest and lowest values, so readers can see the range.
In practice
Real-world examples
Example 1
A recruitment agency pays commission to 8 consultants, and the total paid in a quarter is $96,000. The mean payment is $12,000, which the managing director uses to set next quarter's budget.
Example 2
A software team reviews how long ten support tickets took to fix: 2, 3, 3, 4, 4, 5, 5, 6, 6 and 12 hours. The total is 50 hours, so the mean is 5 hours, though the single 12-hour ticket pulls the average up.
Example 3
A property investor calculates the mean rent across a block of 20 flats to compare with the local market. She finds that two luxury penthouses have lifted the mean, so she also checks the median before pricing a new unit. She later splits the flats into standard and luxury groups so that each average means something.
Think of it
Imagine a group of friends sharing the bill at a restaurant. Instead of arguing over who ate what, you add up the total cost and divide it equally so everyone pays the same average amount.
Formula
Calculation
Mean = Sum of all values / Number of values
Suppose a shop recorded monthly sales of $42,000, $48,000, $45,000, $50,000 and $55,000. Sum = 42,000 + 48,000 + 45,000 + 50,000 + 55,000 = $240,000. Mean = 240,000 / 5 = $48,000.
Now add a sixth month of $120,000 caused by a one-off bulk order. The new sum is $360,000, so the mean = 360,000 / 6 = $60,000. The median of the six months is (48,000 + 50,000) / 2 = $49,000, which is much closer to normal trading.Case study
Seen in the real world
Stratford Wholesale is an illustrative, fictional food distributor whose sales director reported that the average customer order was $3,200. This looked healthy, and the board approved a plan to reduce the sales team.
An analyst questioned the figure and found that 8 of the 200 customers placed enormous orders worth around $50,000 each, while most customers ordered between $500 and $1,500. The median order was just $900.
The board revised the plan to protect the sales staff who served the many smaller accounts, which together produced most of the profit. The illustrative lesson is that a mean should always be tested against the spread of the data before major decisions are made. The analyst now includes the median and the range in every sales report, so that the board can see both the typical order and the effect of the largest customers.
Watch out
Common mistakes
- Using the mean when the data contains extreme values, which can make the figure unrepresentative of typical results.
- Averaging percentages or ratios directly without weighting, which can give a misleading answer when the bases differ.
- Ignoring the number of data points, when a mean based on three values is far less reliable than one based on three hundred.
Questions
People also ask
What is the difference between the mean and the median?
The mean adds up all values and divides by the count, while the median is the middle value when the numbers are sorted.
When should a weighted mean be used?
Whenever the values contribute unequally, such as averaging unit costs across purchases of different sizes.
Is average always the same as mean?
In everyday use yes, but strictly the average can refer to the mean, median or mode, so it is wise to state which is meant.