How this instrument works
An average compresses a list into one representative number. The arithmetic mean does it by the most democratic rule available: every value contributes equally. Add them all, divide by the count. For the list 2, 4, 6, 8 the sum is 20, there are 4 values, and 20 ⁄ 4 = 5. Picture the numbers as equal weights placed along a ruler — the mean is the point where the ruler balances.
Because every value votes, one extreme entry can swing the result hard. The mean of 2, 4, 6 and 88 is 25 — larger than three of the four numbers that produced it. That sensitivity is a property, not a flaw: totals, budgets, and physical measurements want the mean precisely because it accounts for every unit. Skewed data — incomes, house prices, hospital stays — often reads better through the median, which does not care how extreme the extremes are.
This instrument reports the sum and the count beside the mean because they are the working, not decoration. The sum is what you would check against a receipt or a ledger; the count catches the classic slip of a missed or doubled entry. If either looks wrong, the average is wrong too — and you can see exactly where.
- Enter your values in the Numbers field, separated by commas, spaces, or new lines.
- Read the mean (x̄) in the main display; the sum (Σx) and count (n) sit beside it.
- Paste a fresh list or edit a single value — all three results recompute immediately.
- When checking work, scan the count first: a wrong n means a value was missed or typed twice.
Worked example — four rain-gauge readings
A garden rain gauge collects 2, 4, 6, and 8 millimetres on four consecutive days. Sum: 2 + 4 + 6 + 8 = 20 mm. Count: 4 readings. Mean: 20 ⁄ 4 = 5 mm per day — the steady daily fall that would have delivered the same water over the same four days.
These four values are evenly spaced, which unlocks a mental shortcut: for any evenly spaced list, the mean is the first value plus the last, halved. (2 + 8) ⁄ 2 = 5 — the same answer with no adding. The instrument does the full sum regardless, so the shortcut becomes a quick way to check it at a glance.
Questions
What is the difference between the mean and the median?
The mean adds every value and divides by the count; the median is the middle value once the list is sorted. They agree on symmetric data and split apart on skewed data. For 2, 4, 6, 8 both come out at 5 — but change the 8 to 80 and the mean jumps to 23 while the median holds at 5. Reach for the median when a few extremes would misrepresent the typical case.
Can I average negative numbers?
Yes — the formula does not care about sign. Sum the values, negatives included, and divide by the count. The readings −5 and 5 average to exactly 0, and a run of temperatures like −3, −1, 2 averages to −0.67. A negative result simply means the values sit below zero on balance.
How do I calculate a weighted average?
Multiply each value by its weight, sum those products, then divide by the sum of the weights — not by the count. A grade of 80 on an exam worth 70% and 60 on homework worth 30% gives (80 × 0.7 + 60 × 0.3) ⁄ 1 = 74. The plain mean, 70, would be wrong because the two marks do not count equally. This sheet computes the unweighted mean; every value carries weight 1.
Why is my average of averages wrong?
Averaging two group averages only works when the groups are the same size. If a class of 10 students scores 90 on average and a class of 30 scores 70, the true overall figure is (10 × 90 + 30 × 70) ⁄ 40 = 75 — not the 80 you get by averaging 90 and 70. Whenever group sizes differ, go back to the raw material: total sum divided by total count.
Does the order of the numbers matter?
No. Addition is commutative, so 8, 2, 6, 4 gives the identical sum, count, and mean as 2, 4, 6, 8. Order matters for the median (which sorts first) and for running averages tracked over time, but the plain arithmetic mean treats the list as a bag of values, not a sequence.