Descriptive Statistics

How to use this category

Descriptive statistics answer what the batch looks like before anyone tests a hypothesis. On this shelf the mean is an equal share, the median is a position, and the mode is a tally. Spread is split into range, interquartile range, variance, standard deviation, and the more resistant median absolute deviation, because those words are not synonyms. Quartiles follow the type 7 position and say so. A z-score page converts a raw score, and the raw-score page runs the algebra in the other direction. Start here when the question is still about the numbers you hold, not about a p-value.

Bring raw numbers here before you bring a theory. If you have a list, start with the descriptive statistics page when you want the whole portrait, then open the single-purpose page that matches the sentence you will actually publish. A lab report that says the mean was 10.6 from five readings should be able to show the sum was 53. A pay survey that says the median wage should be able to show the ordered middle, not a trimmed mean that nobody mentioned. Z-scores belong in this group when the question is where one score sits against a known mean and spread. They do not belong in a test until you have a hypothesis. Frequency tables and the empirical rule are descriptive even though they feel like probability, because they describe the batch you typed rather than a model you assumed.

The cards above are the whole category, with one sentence on the job each page actually does. Open a page when that sentence matches the decision in front of you. If the sentence is close but the assumption is wrong, read the comparison section on the page before you copy a number into a report, a bid, or a lesson plan.

Worked examples are prefilled so the first result is auditable. Change one input and the ticket updates. The essay under the ticket walks the same arithmetic in sentences, then a second example, then the move that most often breaks the definition. Five questions at the end answer the objections a careful reader raises after seeing the figure. That structure is repeated because the habit of checking is the point, not because the formulas are the same.

Internal links leave this category only when the next formula genuinely lives next door. A standard deviation page may point at variance and at a t test. It should not point at a decking calculator. If you arrived from search on a broad word, use the one-sentence descriptions to discard the near misses. Near misses are how people report a p-value from a test they did not run.

Each worksheet in Descriptive Statistics keeps one H1, a canonical URL that matches the tool name, and meta text sized for search snippets. The steps are part of the page, not a hidden modal. If you teach from these pages, project the ticket and the assumptions together so students see the same definition you graded against.

When two tools in Descriptive Statistics look alike, read the blurb under each name before you commit. The difference is usually a divisor, a critical value, a waste percent, or a caution that belongs on one page and not the other. That difference is why the URLs stay separate.

Reviewed 21-10-2026. Pages in Descriptive Statistics currently include 5 Number Summary Calculator, Arithmetic Mean Calculator, Average Calculator, Coefficient of Variation Calculator, Descriptive Statistics Calculator, Geometric Mean Calculator, Grouped Data Mean Calculator, Harmonic Mean Calculator, Interquartile Range Calculator, Kurtosis Calculator, Lower and Upper Fence Calculator, Mean Absolute Deviation Calculator, Mean Calculator, Mean Median Mode Calculator, Median Absolute Deviation Calculator, Median Calculator, Midrange Calculator, Mode Calculator, Pooled Standard Deviation Calculator, Pooled Variance Calculator, Quartile Calculator, Range Calculator, Root Mean Square Calculator, Skewness Calculator, Standard Deviation Calculator, Standard Error Calculator, Standard Error of Proportion Calculator, Sum of Squares Calculator, Variance Calculator, Weighted Mean Calculator, Z-Score Calculator.

Every descriptive statistics page

• 5 Number Summary Calculator Orders the list and reports the minimum, lower quartile, median, upper quartile, and maximum with Hyndman-Fan type 7 quartiles.
• Arithmetic Mean Calculator Leads with the ordinary mean and, when every value is positive, adds the geometric and harmonic means as comparisons.
• Average Calculator Averages every typed value, or drops one high and one low first when the trim box is ticked and at least three values are present.
• Coefficient of Variation Calculator Divides the sample standard deviation by the mean, and compares a second list when one is pasted.
• Descriptive Statistics Calculator Reports mean, median, mode, variance, standard deviation, range, and five-number summary together.
• Geometric Mean Calculator Averages logarithms and exponentiates the result, and rejects any value that is zero or negative.
• Grouped Data Mean Calculator Estimates a mean from class midpoints and frequencies, and rejects a class whose upper bound is below its lower bound.
• Harmonic Mean Calculator Divides the count by the sum of the reciprocals, and rejects zero or negative values.
• Interquartile Range Calculator Subtracts the lower quartile from the upper quartile and shows that gap as a share of the full range.
• Kurtosis Calculator Reports sample excess kurtosis, shifted so a normal-shaped sample lands near zero.
• Lower and Upper Fence Calculator Builds the 1.5 IQR fences and the 3 IQR extreme fences, then names every pasted point that falls outside.
• Mean Absolute Deviation Calculator Averages the absolute distances from the arithmetic mean, and does not switch the center to the median.
• Mean Calculator Splits a total into an equal share per observation and shows the sum and the count.
• Mean Median Mode Calculator Puts the equal share, the middle rank, and the most repeated value on one ticket, and notes when they disagree.
• Median Absolute Deviation Calculator Takes the median of the absolute distances from the median, then scales that result by 1.4826.
• Median Calculator Sorts the list and returns the middle value, averaging the two middle values when the count is even.
• Midrange Calculator Averages the minimum and the maximum, and also averages the two quartiles as the midhinge.
• Mode Calculator Counts repeats and reports every value that ties for the highest frequency.
• Pooled Standard Deviation Calculator Combines two sample standard deviations into one spread and also reports the standard error of the difference of means.
• Pooled Variance Calculator Weights two sample variances by their degrees of freedom and headlines the combined variance.
• Quartile Calculator Finds Q1, Q2, and Q3 with Hyndman-Fan type 7 and reports the position each quartile came from.
• Range Calculator Subtracts the minimum from the maximum and, when the extremes do not cancel, scales that gap by their sum.
• Root Mean Square Calculator Takes the square root of the average square, and prints the arithmetic mean beside it as a comparison.
• Skewness Calculator Computes adjusted Fisher-Pearson skewness from cubed standardized scores and names the skew band.
• Standard Deviation Calculator Reports the square root of the average squared distance from the mean, using n minus 1 unless the population box is ticked.
• Standard Error Calculator Computes the standard error of a mean from a standard deviation and sample size.
• Standard Error of Proportion Calculator Reports the standard error of a sample proportion using p and n, or a hypothesized p0.
• Sum of Squares Calculator Adds the squared distances from the mean and, beside that corrected total, adds the plain squares of the values.
• Variance Calculator Shows the sample variance and the population variance of one list side by side, and leads with the sample figure.
• Weighted Mean Calculator Averages values that do not get equal votes, using the weight typed beside each value, and shows each weight's share.
• Z-Score Calculator Converts a raw score into how many standard deviations it sits from the mean.