The Descriptive Statistics Calculator takes one pasted data set and returns a full summary: count, sum, minimum, maximum, range, mean, median, mode, variance, standard deviation, standard error, quartiles, interquartile range, outlier bounds, skewness and excess kurtosis. Paste values separated by commas, spaces or line breaks; the calculator computes every measure in one pass and shows the figures in grouped panels.
This page reports. The Mean Median Mode Calculator, Standard Deviation Calculator, Variance Calculator and Quartile Calculator own the teaching for those measures. Links below point to the page that explains each formula in depth.
Summarise a data set in one calculation
Descriptive statistics turn a raw list into a compact portrait: how many values, where they centre, how far they spread, and whether the shape leans or has heavy tails. One paste drives every output, so a single transcription error can move several figures at once. Check the reported count against what you intended before reading further.
Group the outputs by role when you read them: identity (count, sum), centre, spread, position, then shape. Jumping straight to skewness while the count is wrong wastes time. The same paste feeds the box plot and histogram, so a corrected list refreshes every panel together.
Commas, spaces, tabs, line breaks, semicolons and pipes all separate values. A spreadsheet column pastes without reformatting. Non-numeric tokens stop the run with a message naming the offending fragment.
Read the count, sum, minimum, maximum and range
These five figures form the first results panel and the fastest sanity check after a paste. Count is how many values were accepted; sum is their total; minimum and maximum are the extremes; range is maximum minus minimum.
If the count disagrees with the list you meant to analyse, stop before reading centre or spread, because every later figure inherits that error.
Count (n) is how many values were accepted. Sum is their total. Minimum and maximum are the extremes. Range is maximum minus minimum.
For 12, 15, 15, 18, 22, 24, 31: n = 7, sum = 137, min = 12, max = 31, range = 19. If the count is wrong, every later measure is wrong too. Fix the paste before interpreting the mean or the standard deviation.
Read the measures of centre
Centre answers where a typical value sits inside the list. The panel reports mean, median, mode and, when every value is positive, geometric mean. Mean divides the sum by n; median takes the middle of the sorted list; mode is the most frequent value.
On skewed data those three diverge, and that gap is part of the summary rather than a problem to hide.
- Mean = Σx / n (here 137 ÷ 7 ≈ 19.571)
- Median = middle of the sorted list (here 18)
- Mode = most frequent value (here 15)
- Geometric mean when every value is positive
Mean sits above median on this set because the right side stretches to 31. That gap is a first hint of right skew. For definitions, odd/even median rules and mode edge cases, use the Mean Median Mode Calculator. This panel simply prints the numbers for the pasted list.
Read the measures of spread
Spread answers how tightly the values cluster around their centre. The panel reports sample and population variance, sample and population standard deviation, standard error of the mean, and the coefficient of variation as a percentage of the mean. Defaults follow the sample forms that divide by n minus 1 unless you switch the control to population for a complete group.
Defaults follow the sample forms (divide by n − 1) unless you switch to population. On seven values the sample-versus-population gap is visible; on hundreds it shrinks. Full formula walkthroughs live on the Variance Calculator and Standard Deviation Calculator. Standard error equals s / √n and shrinks as n grows.
Read the measures of position
Position measures locate cuts in the ordered list rather than describing average distance from the mean. The panel reports first quartile, median, third quartile, interquartile range and the common outlier fences built from 1.5 times IQR. The active quartile method is named beside Q1 and Q3 so a textbook using another definition can be matched.
lower = Q1 − 1.5 × IQR
upper = Q3 + 1.5 × IQRThe Quartile Calculator documents exclusive, inclusive and interpolation methods. This summary names the active method in the results panel so a textbook mismatch is diagnosable rather than mysterious.
Read skewness and kurtosis
Skewness measures asymmetry around the mean, while excess kurtosis compares tail weight with a normal curve. Near-zero skewness means roughly symmetric data; positive skew means a longer right tail; negative skew means a longer left tail. Excess kurtosis above zero signals heavier tails than normal; below zero signals lighter tails. On small n both estimates wobble.
Kurtosis here is excess kurtosis: positive values indicate heavier tails than a normal distribution; negative values indicate lighter tails. Excess kurtosis of a normal distribution is 0 by definition. On small n both skewness and kurtosis are noisy; treat them as directional hints until the sample is larger.
Summarise the data set 12, 15, 15, 18, 22, 24, 31
This seven-value list is small enough to check by hand and large enough to show centre, spread and position disagreeing in useful ways. Sorted order is 12, 15, 15, 18, 22, 24, 31. The table below lists the main outputs returned in one pass; each figure can be recomputed from the formulas on the linked dedicated pages.
| Measure | Value |
|---|---|
| Count | 7 |
| Sum | 137 |
| Minimum | 12 |
| Maximum | 31 |
| Range | 19 |
| Mean | 19.571 |
| Median | 18 |
| Mode | 15 |
| Sample variance | ≈ 45.95 |
| Sample SD | ≈ 6.78 |
| Q1 (exclusive) | 15 |
| Q3 (exclusive) | 24 |
| IQR | 9 |
Mean 19.571 sits above median 18, matching a mild right lean. Mode 15 is the repeated lower value. IQR 9 covers the middle half from 15 to 24.
Read the box plot and histogram
The box plot draws a box from Q1 to Q3 with a line at the median. Whiskers extend to the farthest points inside the 1.5 × IQR fences; points beyond those fences plot as outlier dots. Reading left to right (or bottom to top on a vertical box) shows the five-number summary at a glance.
The histogram bins the same values into intervals and counts how many fall in each. Bin width affects the picture: too wide hides peaks; too narrow looks noisy. On seven points the histogram is coarse by nature. Use it to see modality and skew, not fine structure. Together, box plot and histogram answer whether the mean is a fair centre or whether the shape warns you off.
Identify outliers in a data set
A point beyond Q1 − 1.5 × IQR or Q3 + 1.5 × IQR is a mild outlier. Beyond 3 × IQR is often labelled extreme. On the worked set, fences sit at 15 − 13.5 = 1.5 and 24 + 13.5 = 37.5, so 31 is inside and no outlier is flagged.
Document every removal. A lab notebook that says "removed outliers" without listing them cannot be checked. Prefer reporting results with and without a contested point when the decision is ambiguous.
Outliers are candidates for investigation, not automatic deletions. A typing error (310 instead of 31) should be fixed. A real extreme measurement should stay unless the analysis plan says otherwise. Removing points silently to "clean" a mean is a common source of biased results. Flag them, document them, then decide.
When to open a dedicated calculator instead
The summary is built for breadth: one paste, many numbers. Depth lives elsewhere by design. Open the Mean Median Mode Calculator when the question is which centre measure to trust. Open the Variance or Standard Deviation Calculator when the question is sample versus population or the sum-of-squares table.
Open the Quartile Calculator when Q1 disagrees with a solution key and the method must change.
That separation also protects search intent. A reader who typed a full descriptive-statistics query wants the overview. A reader who typed sample standard deviation wants Bessel's correction, not a second copy of it buried inside a mega-summary.
Frequently asked questions
What are descriptive statistics?
Descriptive statistics summarise a data set without inferring about a larger population. Typical outputs include count, centre (mean, median, mode), spread (range, variance, standard deviation, IQR), position (quartiles) and shape (skewness, kurtosis).
How is this different from the Mean Median Mode Calculator?
That page teaches and emphasises the three centre measures, plus range and sum. This page returns those measures as one row in a wider summary that also includes spread, quartiles, outliers and shape.
Does the calculator use sample or population formulas?
Sample formulas (n − 1) are the default for variance and standard deviation. Switch to population when the data really is the entire group. The results panel labels which form is active.
What quartile method is used?
The default matches the Quartile Calculator default (exclusive / Tukey-style hinges, Excel QUARTILE.EXC). Other methods are selectable. Small data sets can disagree across methods; the method name is always shown beside Q1 and Q3.
What is skewness?
Skewness measures asymmetry. Positive skew means a longer right tail; negative skew means a longer left tail; near zero means roughly symmetric. Compare mean and median as a quick check: mean above median often accompanies positive skew.
What is excess kurtosis?
Excess kurtosis compares tail weight to a normal distribution. Zero matches normal tails; positive means heavier tails; negative means lighter tails. On small samples the estimate wobbles, so read it cautiously.
How are outliers detected?
Points outside Q1 − 1.5 × IQR or Q3 + 1.5 × IQR are flagged as mild outliers. The 3 × IQR rule marks extremes. Flags are alerts for review, not automatic removals.
Can I paste a spreadsheet column?
Yes. Newline-separated, tab-separated, comma-separated and mixed separators are accepted. Confirm the count after pasting.
Is anything stored or sent?
No. Calculation runs in the browser. Nothing is uploaded. Export is only what you copy yourself.
Summary
The Descriptive Statistics Calculator summarises one pasted data set into count, centre, spread, position and shape measures in a single pass, with box plot and histogram views for distribution shape. Sample variance and standard deviation are the defaults; quartile method is named in the output.
Use this page for a full portrait. Open the dedicated mean, variance, standard deviation or quartile pages when you need the teaching walkthrough behind a single measure.