To calculate an average, add up all the numbers in your set and divide by how many numbers there are. If your values are 8, 12, and 10, the sum is 30, and dividing by 3 gives you an average of 10. That core formula covers most everyday situations, but “average” can mean different things depending on context. Here’s how each type works and when to use it.
The Basic Formula
The standard average, formally called the arithmetic mean, follows a three-step process:
- Add all the values together. This gives you the total sum.
- Count how many values you have. This is your number of data points.
- Divide the sum by the count. The result is your average.
Written as a formula: Average = (x₁ + x₂ + x₃ + … + xₙ) ÷ n, where each x is a value and n is the total number of values.
Say you scored 85, 90, 78, and 95 on four tests. Add them up: 85 + 90 + 78 + 95 = 348. Divide by 4. Your average score is 87.
When a Simple Average Misleads You
A simple average treats every value equally, which can distort the picture when a few extreme numbers pull the result up or down. Wage data from the Social Security Administration illustrates this well: the median wage (the value right in the middle when you line up all workers from lowest to highest paid) is substantially less than the average wage. That gap exists because a small number of very high earners push the average upward, making it look like a typical worker earns more than they actually do.
This is why news reports about income, home prices, or wealth often use the median instead of the mean. The median isn’t affected by outliers. If you have five home sale prices of $200K, $210K, $220K, $230K, and $1.2M, the average is $412K, but the median is $220K, which better reflects what a typical home sold for.
The mode, another type of average, is simply the value that appears most often. If a shoe store sells sizes 8, 9, 9, 9, 10, and 11, the mode is 9. It’s most useful when you care about the most common outcome rather than a mathematical center point.
How to Calculate a Weighted Average
A weighted average accounts for the fact that some values matter more than others. In a weighted average, each number is multiplied by a predetermined weight before you add everything up and divide.
Grade point averages work this way. A 4-credit class counts more toward your GPA than a 1-credit class. If you earned an A (4.0) in a 4-credit course and a B (3.0) in a 2-credit course, you wouldn’t just average 4.0 and 3.0 to get 3.5. Instead:
- Multiply each grade by its credits: (4.0 × 4) + (3.0 × 2) = 16 + 6 = 22
- Divide by total credits: 22 ÷ 6 = 3.67
The same logic applies in investing. If you buy 100 shares of a stock at $10 and later buy 50 more shares at $40, a simple average of the two prices would be $25. But you bought more shares at the lower price, so the weighted average reflects that. Multiply 100 shares by $10 ($1,000) and 50 shares by $40 ($2,000), add those together ($3,000), then divide by your total 150 shares. Your weighted average cost per share is $20, not $25.
Moving Averages for Tracking Trends
A moving average applies the same basic formula but recalculates it over a rolling window of time. It’s commonly used to smooth out noisy data so you can spot a trend.
To calculate a simple moving average (SMA), pick a number of periods (say, 10 days), add up the values for those 10 days, and divide by 10. Each new day, you drop the oldest value and add the newest one, then recalculate. The formula is the same as any arithmetic mean: SMA = (A₁ + A₂ + … + Aₙ) ÷ n.
If you’re tracking daily sales for the past 5 days and your totals are $400, $450, $380, $420, and $500, the 5-day moving average is $430. Tomorrow, you’d drop $400, add the new day’s number, and divide by 5 again. An upward-trending moving average tells you values are generally rising, while a downward-trending one signals a decline. Investors use moving averages on stock charts to filter out day-to-day volatility and focus on the broader direction.
Calculating Averages in Spreadsheets
You don’t need to do the math by hand. Excel and Google Sheets both have built-in functions that handle averages instantly.
For a standard average, type =AVERAGE(A1:A10) to average all values in cells A1 through A10. You can also list values directly: =AVERAGE(85, 90, 78, 95). The function ignores any cells containing text and only works with numbers.
For a median, use =MEDIAN(A1:A10). This returns the middle value in the range, which is helpful when your data has outliers you don’t want skewing the result.
Google Sheets offers an AVERAGE.WEIGHTED function for weighted averages. In Excel, you can replicate a weighted average with =SUMPRODUCT(A1:A10, B1:B10) / SUM(B1:B10), where column A holds the values and column B holds the weights. SUMPRODUCT multiplies each value by its corresponding weight and sums the results, and dividing by the total of the weights gives you the weighted average.
Choosing the Right Type of Average
The method you pick depends on what you’re trying to understand. Use a simple arithmetic mean when your data points are roughly similar in size and none of them carry more importance than the others. Use a weighted average when some data points should count more, like credit hours in a GPA or share quantities in a portfolio. Use a median when extreme values could distort the picture, such as income data or home prices. And use a moving average when you want to track how a value is changing over time rather than summarize a fixed set of numbers.
In every case, the underlying principle is the same: you’re compressing a set of numbers into a single representative value. The skill is knowing which representative value tells the most honest story for your situation.