Average Calculator: Mean, Median, Sum & Range

Mean, median, and when each one lies

The average most people mean is the arithmetic mean: add everything up and divide by the count. It uses every value, which is its strength and its weakness. One extreme number drags it hard.

Take five salaries: $40,000, $45,000, $50,000, $55,000, and $300,000. The mean is $98,000, a salary nobody in the group earns. The median, the middle value once sorted, is $50,000, which describes the typical person far better. That is why US household income is reported as a median. If mean and median are far apart, your data is skewed, and the median is usually the honest number to quote.

Worked example: test scores

Scores of 85, 92, 78, 90, and 88. Sum: 433. Count: 5. Mean: 433 ÷ 5 = 86.6. Sorted, the list is 78, 85, 88, 90, 92, so the median is 88. The range is 78 to 92, a spread of 14 points.

With an even count there is no single middle value, so the median is the mean of the two middle numbers. Add a sixth score of 70 and the sorted list becomes 70, 78, 85, 88, 90, 92. The median is (85 + 88) ÷ 2 = 86.5 and the mean drops to 503 ÷ 6 = 83.8. The low score moved the mean by almost 3 points but the median by only 1.5.

Weighted averages: grades, GPA, and prices

A plain average assumes every value counts equally. Often they don't. If a midterm is worth 40 percent and a final 60 percent, scores of 90 and 80 give (90 × 0.4) + (80 × 0.6) = 84, not the 85 a simple average would suggest.

GPA works the same way with credit hours as weights: an A (4.0) in a 4-credit class and a B (3.0) in a 2-credit class give (16 + 6) ÷ 6 = 3.67, not 3.5. The GPA calculator and grade calculator handle those weights for you. For investors, the average price paid across several purchases must be weighted by shares bought, or the cost basis comes out wrong.

Averaging percentages and rates

Percentages from groups of different sizes can't be averaged directly. If 50 percent of 10 people and 90 percent of 90 people said yes, the overall rate is (5 + 81) ÷ 100 = 86 percent, not the 70 percent a naive average gives.

Speeds and other rates trip people up too. Drive 60 miles at 30 mph and 60 miles back at 60 mph and your average speed is not 45 mph. Total distance is 120 miles, total time is 2 hours plus 1 hour, so it is 40 mph. For rates over equal distances, use the harmonic mean or, simpler, total distance over total time. Investment returns need the geometric mean: +50 percent then −50 percent averages to 0 percent arithmetically, but you actually lost 25 percent.

Entering data cleanly

Separate numbers with commas, spaces, semicolons, or new lines. You can paste a column straight from a spreadsheet. Because commas separate values, type 1500 rather than 1,500, or the tool reads 1 and 500 as two numbers. Blank lines and trailing commas are ignored rather than counted as zeros, a bug that quietly skews results in some calculators.

Before trusting any average, glance at the range. A minimum of 0 in a list of prices, or a maximum ten times bigger than everything else, often means a typo or a missing value coded as zero. Fix or remove it, then compare the mean and median again.

Which number to report

Use the mean when values are roughly symmetric and you care about totals: average order value, average monthly spending, class average. Use the median for skewed data such as income, home prices, and response times. Report the count alongside either one; an average of three numbers deserves less confidence than an average of three hundred. For spread, the standard deviation calculator tells you how tightly values cluster around the mean.