Quick answer: the mean is the sum divided by the count: 4 + 8 + 15 + 16 + 23 + 42 = 108, and 108 ÷ 6 = 18. The median is the middle value when sorted – with six numbers it’s the average of 15 and 16, so 15.5. The mode is the most frequent value.
Mean, median or mode – which average?
| Average | How | Best for |
|---|---|---|
| Mean | Sum ÷ count | Marks, temperatures, everyday averages |
| Median | Middle value when sorted | Salaries and house prices, where a few huge values pull the mean up |
| Mode | Most common value | Shoe sizes, survey answers, the “usual” value |
In the example list, one large value (42) drags the mean (18) above the median (15.5). That gap is a quick sign your data is skewed.
Standard deviation: how spread out are the numbers?
Standard deviation measures the typical distance from the mean. Two classes can both average 70%, but one with a standard deviation of 3 has everyone close to 70 while one with 20 has top students and struggling ones.
- Population standard deviation divides by n – use it when your list is the whole group (every student in the class).
- Sample standard deviation divides by n − 1 – use it when your list is a sample of a bigger group (50 customers out of thousands). This is what Excel’s STDEV.S gives.
For the example: population SD ≈ 12.32, sample SD ≈ 13.49.
Geometric mean
For growth rates and ratios the geometric mean is the right average: returns of +50% and −50% average to 0% arithmetically, but you actually lost 25%. The calculator shows it whenever all numbers are positive.
For credit-weighted grades, the GPA calculator applies the credit hours for you. To turn an average into a percentage of a total, use the percentage calculator.
How to find the average of numbers
- Paste or type your numbers. Separate them with commas, spaces or new lines – a pasted spreadsheet column works.
- Read the mean. The arithmetic average appears at the top.
- Check median and mode. Compare them with the mean to spot skewed data or repeated values.
- Use the spread figures. Range and standard deviation show how far the values are from each other.
Weighted average: when items don’t count equally
A course grade is 30% coursework (you scored 72) and 70% final exam (you scored 85). The simple average, 78.5, is wrong because the parts have different weights.
- Multiply each score by its weight: 72 × 0.30 = 21.6 and 85 × 0.70 = 59.5.
- Add them: 21.6 + 59.5 = 81.1.
- If the weights don’t add up to 1 (or 100%), divide by their total.
Common averaging mistakes
- Averaging averages from groups of different sizes – combine the totals instead.
- Using the mean for skewed data such as incomes – the median is more representative.
- Averaging percentages of growth – use the geometric mean for rates of return.
Frequently asked questions
How do I calculate the average of numbers?
Add all the numbers and divide by how many there are. 10, 20 and 30 add up to 60; 60 ÷ 3 = 20.
How do I find the median?
Sort the numbers. With an odd count, take the middle one; with an even count, average the two middle ones.
What if there is no mode?
If every value appears once, there is no mode. If several values tie, they are all modes.
Which standard deviation should I use?
Population (÷ n) for a complete group, sample (÷ n − 1) when the numbers are a sample of a larger group.
Can I paste numbers from Excel?
Yes. Copy a column or row and paste it in; line breaks and tabs are handled.
Does it handle decimals and negative numbers?
Yes, both work. Use a dot for decimals (2.5), since commas separate numbers.
How do I calculate a weighted average?
Multiply each value by its weight, add the results and divide by the sum of the weights. Coursework 72 at 30% and exam 85 at 70% gives 81.1.
What is the difference between average and median?
The average (mean) adds everything and divides by the count; the median is the middle value. Large outliers move the mean but hardly change the median.