How do you calculate an average?
Add all the values, then divide by how many there are. For 72, 85, 90, 68 and 80 the total is 395, and 395 ÷ 5 = 79. That is the mean, the number most people call the average.
Average Calculator
The mean, median and mode of your numbers, and how spread out they are.
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Right answer?
Your answer
The middle of your numbers
Type your list of numbers and the mean, median, mode and range appear here, each with its working.
The working
Mean = total ÷ count
| Measure | How | Your result |
|---|---|---|
| Mean | 731 ÷ 9 | 81.2222 |
| Median | Middle value once sorted | 84 |
| Mode | Most frequent value(s) | 85 |
| Quartiles | Median of the lower half and of the upper half | Q1 74, Q3 87.5 |
| IQR and fences | Q3 − Q1; fences 1.5 × IQR beyond each quartile | 13.5; 53.75 to 107.75 |
| Variance | Squared distances from the mean ÷ (count − 1) | 62.1944 |
| Standard deviation | Square root of the variance (population: divide by count) | 7.8863 (population 7.4353) |
| Trimmed mean | Drop 0 from each end, then average | 81.2222 |
Worked examples
- Test scores 72, 85, 90, 68, 80: total 395, so the mean is 395 ÷ 5 = 79. Sorted (68, 72, 80, 85, 90), the median is 80. No score repeats, so there is no mode.
- 3, 7, 7, 19: mean 36 ÷ 4 = 9; median (7 + 7) ÷ 2 = 7; mode 7. The lower half 3, 7 gives Q1 = 5 and the upper half 7, 19 gives Q3 = 13.
- 1, 2, 3, 4, 100: the mean is 110 ÷ 5 = 22, but the median is 3. The sample standard deviation is 43.6, almost all of it from the 100. This is why incomes and house prices are usually quoted as medians.
- Prices weighted by sales: 10 sold at $5 and 90 sold at $9. The plain mean of the two prices is $7, but the average price paid is (10 × 5 + 90 × 9) ÷ 100 = $8.60. Enter it as two rows in Value × count: “5 10” and “9 90”.
Good to know
Mean, median and mode answer different questions
The mean uses every value, so it is the best summary when the values are balanced, and the one most easily pulled by a single extreme value. The median only cares about position, so one very large number barely moves it. The mode tells you what is most common, which is the useful answer for things like shoe sizes or survey choices.
- Averages of averages go wrong. 80% on a 5-question quiz and 60% on a 100-question exam do not average to 70% if every question counts equally. Add the marks first: (4 + 60) ÷ 105 = 61%.
- Zero is a value. Leave a number out only if it is missing.
- Decide what counts equally. If every test should count the same, turn each mark into a percentage first (43 out of 50 is 86%; the percent calculator does it) and average those. If every question should count the same, add the marks instead, as above.
- Name the quartile method. Spreadsheets may interpolate, so short lists can give slightly different quartiles.
- Sample or whole group? Use the sample standard deviation (count − 1) when your numbers are a sample of something bigger, and the population figure when they are the whole group.
- A trimmed mean drops the same share from both ends before averaging. Judged sports and some economic figures use it to soften extreme values without ignoring the rest.
Questions
Questions people ask about averages
What is the average of 85 and 90?
87.5. Add the two numbers and halve the total: 85 + 90 = 175, and 175 ÷ 2 = 87.5. The average of any two numbers is the point exactly halfway between them. The Two numbers tab does this for any pair.
What score do I need to get the average I want?
Multiply the average you want by the total number of scores, then take away what you already have. With 72, 80, 78 so far and one test to go, an average of 80 needs 80 × 4 = 320 in total. You have 230, so the last test must bring 90. The Target tab works this out for any number of tests and tells you when a target is out of reach.
What is the difference between mean, median and mode?
The mean is the total divided by the count. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. For 1, 2, 2, 3 and 100 the mean is 21.6, the median is 2 and the mode is 2.
Should I use the mean or the median?
Use the mean when the values are fairly balanced. Use the median when one or two values are far from the rest, such as house prices or incomes, because a single extreme value pulls the mean but barely moves the median.
Can there be no mode, or more than one?
Yes to both. If every value appears once, there is no mode. If two or more values tie for most often, they are all modes: 1, 2, 2, 3, 3, 4 has modes 2 and 3.
Does zero count in an average?
Yes. A zero is a real value: it adds nothing to the total but still counts as one value. The average of 10, 0 and 20 is 30 ÷ 3 = 10. Leave a value out only if it is missing, not if it is zero.
Why are my quartiles different from my spreadsheet?
There are several accepted ways to find quartiles. This calculator takes the median of the lower half and of the upper half. Spreadsheets often interpolate instead, which can give slightly different answers on short lists.
Print room
Three one-page sheets, or the whole thing in Excel
The summary for homework or a report, a score tracker to keep filling in by hand, or the target planner for the next tests. Each sheet carries today's date and the page address. The Excel file has your numbers with every result as a live formula, so adding a score recalculates the lot.
For spreadsheets and code
The same summary in Python and JavaScript
import math
data = [68, 72, 76, 80, 84, 85, 85, 90, 91]
data.sort()
mean = sum(data) / len(data)
mid = len(data) // 2
median = data[mid] if len(data) % 2 else (data[mid - 1] + data[mid]) / 2
print(f"count={len(data)}")
print(f"mean={mean}")
print(f"median={median}")
if len(data) < 2:
print("standard_deviation=sample SD needs at least two values")
else:
variance = sum((x - mean) ** 2 for x in data) / (len(data) - 1)
print(f"variance={variance}")
print(f"standard_deviation={math.sqrt(variance)}")
Both snippets use your current numbers and print the count, mean, median, variance and sample standard deviation.
Statistical summary
Name: ______________________ Date: ____________
Data (9 values): 68, 72, 76, 80, 84, 85, 85, 90, 91
| Measure | Working | Result |
|---|---|---|
| Mean | 731 ÷ 9 | 81.2222 |
| Median | Middle value once sorted | 84 |
| Mode | Most frequent value(s) | 85 |
| Quartiles | Medians of the lower and upper halves | Q1 74, Q3 87.5 |
| Spread | Range, IQR, sample SD | 23, 13.5, 7.8863 |
| Outliers | Beyond 53.75 or 107.75 | None |
The mean and median are close, so the mean is a fair summary.
calculationtime.com/calculators/average-calculator/ · Printed 2 November 2026
Sources
Where these methods come from
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