Mean Calculator — Descriptive Statistics

Arithmetic mean is the statistic everyone reports and the one most likely to mislead when the data is skewed. A dataset of seven salaries (six at $40,000, one at $400,000) produces a mean of $91,429, a number that describes nobody in the room. Mean Calculator shows mean, median, mode, range, variance and standard deviation together so the gap between mean and median is immediately visible. When that gap exceeds 5% of the mean, the tool flags the direction of skew and names the median as the more representative centre.

Paste any list of numbers (separated by commas, spaces, semicolons or newlines) and all fifteen statistics update at once. The Population/Sample toggle switches between dividing by N (the full population formula) and dividing by N−1 (Bessel's correction for a sample), which changes variance, standard deviation and the coefficient of variation simultaneously.

Worked Example: the Salary Dataset

Input: 40000, 40000, 40000, 40000, 40000, 40000, 400000(7 values). Mean = $91,428.57; Median = $40,000; Mode = $40,000 (appears 6 times); Range = $360,000; Sample std dev = $135,247. The mean is $51,428.57 (56.3%) above the median; the tool prints the right-skew notice and recommends the median. Q1 = $40,000, Q3 = $40,000, IQR = $0; the interquartile range is zero because six of seven values are identical, which is itself a meaningful finding.

How the Math Works

• Mean: sum of all values divided by count.
• Median: middle value of the sorted list; average of the two middle values for an even count.
• Mode: value(s) appearing most often. Returns "none" when all values are unique; returns multiple values when two or more share the highest frequency.
• Variance: mean of squared deviations from the mean. Sample variance divides by N−1 (Bessel's correction) to give an unbiased estimate; population variance divides by N.
• Standard deviation: square root of variance. Same N vs N−1 distinction applies.
• Q1 / Q3: medians of the lower and upper halves of the sorted list (inclusive method: the central value is excluded from both halves for odd-count datasets).
• Skewness: Pearson's second coefficient: 3(mean − median) / std dev. Positive means right-skewed (long tail on the right); negative means left-skewed.
• CV (coefficient of variation): sample std dev divided by the absolute mean, expressed as a percentage. Shown as "n/a" when the mean is zero.

Tricky Inputs to Watch For

• A single value returns an error: at least 2 numbers are required because sample variance divides by N−1, which is zero for N = 1.
• All identical values (e.g. five 7s) produce a variance of 0, std dev of 0, and IQR of 0. Mode returns that single value. Skewness is 0 because mean equals median exactly.
• Negative numbers are fully supported. Mean of -10, 0, 10 is 0, making CV undefined (displayed as "n/a").
• Decimal inputs are accepted; the parser splits on commas, spaces, semicolons and newlines so 18.4 19.1 21.3 works without commas.
• The tool rejects any token that does not parse as a JavaScript Number, including scientific notation like 1e3; enter plain decimals instead.