The Statistics Calculator takes a pasted list of numbers and returns a complete summary in one pass: count, sum, minimum, maximum, range, mean, median, mode, variance, standard deviation, quartiles and interquartile range. Paste values separated by commas, spaces or line breaks, and every measure computes together from the same list, so a single correction to the data refreshes every figure at once.
Rather than calculating each statistic separately with a different tool, this page runs the full set of standard descriptive measures on one data set, grouped by what they describe: identity, center, spread and position.
Summarize a data set in one calculation
Statistics on a raw list turn it into a compact portrait: how many values there are, where they center, how far they spread, and where the quartile cuts fall. One paste drives every output.
Checking the reported count against what was actually intended is the fastest sanity check before reading any other figure, since a transcription error in the data shifts every downstream statistic.
Read the identity statistics: count, sum, min, max, range
Worked example: the data set 12, 15, 15, 18, 22, 24, 31.
| Measure | Value |
|---|---|
| Count | 7 |
| Sum | 137 |
| Minimum | 12 |
| Maximum | 31 |
| Range | 19 |
Count is how many values were accepted. Sum is their total. Minimum and maximum are the extremes. Range is maximum minus minimum: 31 − 12 = 19.
Read the measures of center: mean, median, mode
| Measure | Value |
|---|---|
| Mean | 19.571 |
| Median | 18 |
| Mode | 15 |
Mean divides the sum by the count: 137 ÷ 7 ≈ 19.571. Median is the middle of the sorted list (12, 15, 15, 18, 22, 24, 31), which is 18, the fourth of seven values. Mode is the most frequent value, 15, which appears twice while every other value appears once.
Mean (19.571) sitting above median (18) is a first hint of mild right skew, since the mean is being pulled upward by the higher values (22, 24, 31) more than the median is.
Read the measures of spread: variance and standard deviation
| Measure | Value |
|---|---|
| Sample variance | ≈ 45.95 |
| Sample standard deviation | ≈ 6.78 |
Sample variance and standard deviation describe how tightly values cluster around the mean, using the sample convention that divides by n − 1 rather than n. A standard deviation of about 6.78, against a mean of about 19.6, indicates a moderate spread relative to the center of the data.
Read the measures of position: quartiles
| Measure | Value |
|---|---|
| Q1 (exclusive method) | 15 |
| Q3 (exclusive method) | 24 |
| IQR | 9 |
The interquartile range, Q3 minus Q1, covers the middle 50 percent of the data: 24 − 15 = 9, spanning the values from 15 to 24. Different quartile methods (exclusive, inclusive, interpolation) can shift Q1 and Q3 slightly, particularly on small data sets like this seven-value example.
Understand how the measures relate to each other
Reading the four groups together, identity, center, spread and position, tells a fuller story than any single statistic alone.
Here, the count and sum confirm the data was entered correctly; the mean-above-median relationship signals mild right skew; the standard deviation of about 6.78 quantifies that spread numerically; and the IQR of 9 shows the middle half of the data is relatively tight even though the full range is 19.
Read the population variance alongside the sample variance
Some assignments call for the population formula instead of the sample formula, dividing by n rather than n − 1. For this same seven-value set, population variance works out to about 39.39, smaller than the sample variance of about 45.95, since dividing by a larger denominator (n = 7 versus n − 1 = 6) always produces a smaller figure.
Population standard deviation follows as the square root, about 6.28 against the sample figure of about 6.78. Checking which formula a course or tool expects avoids a mismatch that looks like an arithmetic error but is really a difference in convention.
Frequently asked questions
What statistics does this calculator compute?
Count, sum, minimum, maximum, range, mean, median, mode, sample variance, sample standard deviation, quartiles (Q1 and Q3), and the interquartile range, all from a single pasted data set.
What is the difference between mean and median in a statistics summary?
Mean is the sum divided by the count; median is the middle value of the sorted data. When they differ noticeably, as with a mean of 19.571 versus a median of 18 in the example, that gap signals the data is not perfectly symmetric.
Why does variance use n − 1 instead of n?
The sample variance formula divides by n − 1 (rather than the population formula's n) to correct for a known bias when estimating a population's variance from a sample rather than measuring the full population directly.
What is the interquartile range used for?
IQR measures the width of the middle 50 percent of the data and is more resistant to distortion from a single outlier than the full range, which only uses the two extreme values.
Can I compute all these statistics from a small data set?
Yes, though for very small data sets some measures, particularly variance, standard deviation, skewness and kurtosis, can be less stable and should be interpreted cautiously.
What does it mean if mean is higher than median?
It typically indicates the data has a longer tail toward higher values (right or positive skew), since a few large values pull the mean upward more than they shift the position-based median.
Do different quartile methods give different results?
Yes. At least four common methods exist for calculating quartiles, and they can produce slightly different Q1 and Q3 values, particularly on small data sets, so checking which method matches a specific textbook or software tool matters when comparing results.
Summary
A complete statistics summary of 12, 15, 15, 18, 22, 24, 31 shows a count of 7, a sum of 137, a mean of about 19.571 against a median of 18 (mild right skew), a mode of 15, a sample standard deviation of about 6.78, and quartiles of 15 and 24 giving an IQR of 9.
Reading identity, center, spread and position together gives a much fuller picture of the data than any single statistic alone.