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Paste 12, 18, 7, 18, 25, 9, 31, 14 → mean 16.75, median 16, mode 18. Weighted mode handles grades: 88, 92, 79 at 3/2/4 credits = 84.89.
The average question looks simple until the data fights back: an outlier drags the mean, the list has an even count so the median splits two values, or every number carries a different weight. This calculator takes a pasted list — commas, spaces, or newlines — and returns every flavor of "average" at once: mean, median, mode, range, standard deviation, and a weighted average when your numbers don't all count equally.
Anyone with a column of numbers uses it: paste 12, 18, 7, 18, 25, 9, 31, 14 and get mean 16.75, median 16, mode 18 — plus weighted average for grades and share lots.
The mean is the arithmetic average — sum divided by count — and it is the right choice for evenly distributed data like test scores or temperatures. The median is the middle value when sorted, and it is the right choice whenever outliers exist: house prices, salaries, and net worth are always reported as medians because one mansion or billionaire drags the mean far from typical. The mode is the most frequent value, useful for categories and inventory (the most-ordered size, the most-common defect). The diagnostic trick: when mean and median disagree significantly, the data is skewed and the median is usually the honest summary. A mean of $95k with a median of $62k in a salary dataset means a few high earners are inflating the "average."
Multiply each value by its weight, sum those products, and divide by the sum of the weights. Grades are the classic case: scores of 88, 92, and 79 in courses worth 3, 2, and 4 credits give (88×3 + 92×2 + 79×4) ÷ 9 = 84.89 — the 4-credit 79 pulls harder than the 2-credit 92. Investors use the identical math for cost basis: 100 shares at $40 and 50 at $55 is an average cost of $45, not $47.50. The common mistake is averaging percentages directly — a portfolio up 20% on $10k and down 10% on $50k is not "up 5%"; weight by dollars and it is down 5%. This calculator runs the weighted mean the moment your weights list matches the count of your numbers.
Because averages hide distribution. The mean is a balance point — every value pulls it — while the median only cares about position, so extreme values move the mean but leave the median untouched. Real estate illustrates it perfectly: five homes sell at $300k, $320k, $340k, $350k, and $1.2M. The mean is $502k; the median is $340k — and $340k is what a typical buyer actually faces. Standard deviation quantifies the spread: a small SD means the mean represents the data well, a large one means it does not. Rule of thumb for reporting: symmetric data → mean; skewed data → median; categories → mode. When in doubt, report both the mean and median — their gap is itself information.