Calculate the average (mean) of values
The average — also called the arithmetic mean — is found by dividing the sum of all values by the number of values. It represents the central value of a dataset.
Average = Sum of all values ÷ Number of values
For example, the average of 10, 20, 30, 40, and 50 is (10+20+30+40+50) ÷ 5 = 150 ÷ 5 = 30.
The average is one of three common measures of central tendency, and they can give very different results for the same dataset:
| Measure | Definition | Best used when |
|---|---|---|
| Mean (average) | Sum divided by count | Data is evenly distributed |
| Median | Middle value when sorted | Data has outliers |
| Mode | Most frequent value | Finding the most common value |
For the dataset 1, 2, 3, 4, 100 — the mean is 22, the median is 3, and the mode does not exist. The median is more representative here because 100 is an outlier that pulls the mean up dramatically.
A classic example: a company has 9 employees earning $30,000 per year and one CEO earning $300,000. The average salary is ($30,000 × 9 + $300,000) ÷ 10 = $57,000 — but 90% of employees earn well below that figure. In cases like this, the median ($30,000) gives a more accurate picture of a typical employee's pay.
Similarly, average speed on a journey with stops does not reflect speed at any given moment. Average rainfall does not tell you whether it rained every day or all at once.
A weighted average assigns different importance to different values. University grades are often weighted — a final exam worth 60% of a course carries more weight than a quiz worth 10%. The weighted average is calculated by multiplying each value by its weight, summing the results, and dividing by the total weight.
For example, a student scores 70 on a quiz (weight 20%) and 85 on a final (weight 80%). Weighted average = (70 × 0.20) + (85 × 0.80) = 14 + 68 = 82.
Add all the numbers together to get the sum, count how many numbers there are, then divide the sum by the count. For example, the average of 4, 8, 15, 16, 23, and 42 is (4+8+15+16+23+42) ÷ 6 = 108 ÷ 6 = 18.
They are the same thing. Mean is the mathematical term; average is the everyday term. Both refer to the sum of values divided by the count of values.
Yes. A single very large outlier can pull the mean above most of the values in the dataset. This is why median is often preferred for income or property price data.
A weighted average gives more importance to some values than others. Multiply each value by its weight, sum the results, and divide by the total weight. University grades and portfolio returns are common examples.
At least two, though technically you can average a single number — the result is just that number itself. More values generally produce a more meaningful average.