Reading a Descriptive Statistics Summary
A good summary answers three questions about your data. Where is its center? (mean, median, mode). How spread out is it? (range, IQR, standard deviation). And are any values suspiciously extreme? (outlier fences). Looking at center and spread together is what makes the numbers meaningful — a mean of 50 with an SD of 2 describes a completely different situation than a mean of 50 with an SD of 30. For deeper dives on individual measures, see our average calculator and standard deviation calculator, which show the step-by-step arithmetic for each.
Outlier fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR
Data: 4, 8, 15, 16, 23, 42. Sorted, the median is (15 + 16) ÷ 2 = 15.5. Lower half (4, 8, 15) gives Q1 = 8; upper half (16, 23, 42) gives Q3 = 23, so IQR = 15. Upper fence = 23 + 22.5 = 45.5 — the 42 is large but not technically an outlier by the 1.5×IQR rule.
Mean vs. Median in Skewed Data
When the mean sits well above the median, the data is right-skewed — a few large values are pulling the average up (incomes, house prices, city sizes). When mean and median nearly agree, the data is roughly symmetric and the mean is a trustworthy summary. Comparing the two is the fastest skew check there is, and this calculator puts them side by side for exactly that reason.
Frequently Asked Questions
What are descriptive statistics?
Numbers that summarize a data set: measures of center (mean, median, mode), spread (range, quartiles, IQR, variance, standard deviation) and shape. They describe the data you have, as opposed to inferential statistics, which draw conclusions about a larger population.
What is the five-number summary?
Minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It splits data into four equal parts and is what a box plot draws. The interquartile range, IQR = Q3 − Q1, spans the middle 50% of the data.
How are quartiles calculated?
This calculator uses the common median-split method: Q1 is the median of the lower half of the sorted data and Q3 the median of the upper half, excluding the overall median itself when the count is odd. Other conventions exist (spreadsheets interpolate differently), so quartiles can differ slightly between tools.
What is standard error of the mean (SEM)?
The standard deviation divided by the square root of the sample size. It estimates how much the sample mean would vary if you repeated the sampling — the basis of confidence intervals and t-tests.
How do I spot outliers with the IQR?
A common rule flags values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as potential outliers. This calculator reports those fences so you can check your data against them.
Cite This Calculator
Using this calculator in an assignment, article or lesson? Copy a ready-made citation — or the link snippet if you're referencing it from a web page.
The CalculatorsGuide Editorial Team. (2026). Statistics Calculator. CalculatorsGuide. Retrieved from https://www.calculatorsguide.com/statistics/statistics-calculator/