Range Calculator
Range Calculator works out Count (n) and Sum from Data set, Quartile method and Outlier fence multiplier. The default figures on this page give range of 7; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
8 steps
- Sorted data (n = 8): 2, 4, 4, 4, 5, 5, 7, 9
- Mean = 40 / 8 = 5
- Median = average of the two middle values = 4.5
- Sum of squared deviations SS = 32
- Sample variance = SS / (n - 1) = 32 / 7 = 4.57142857, so s = 2.13808994
- Population variance = SS / n = 32 / 8 = 4, so sigma = 2
- Quartiles (linear method): Q1 = 4, Q2 = 4.5, Q3 = 5.5, IQR = 1.5
- Outlier fences = Q1 - 1.5 x IQR = 1.75 and Q3 + 1.5 x IQR = 7.75
Modal valuestable
Outlierstable
Five-number summarytable
Sorted datatable
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the Range Calculator calculates
Computes the full descriptive summary of a data set: count, sum, mean, median, mode, range, midrange, sample and population variance and standard deviation, quartiles, interquartile range, percentiles, the five-number summary, Tukey outlier fences, mean and median absolute deviation, coefficient of variation, skewness and excess kurtosis.
How to use this Range Calculator
Enter Data set, Quartile method and Outlier fence multiplier. Count (n) updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Count (n), Sum and Mean.
The method follows NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5 Quantitative Techniques, Hyndman, R.J. & Fan, Y. (1996), "Sample Quantiles in Statistical Packages", The American Statistician 50(4), 361-365, Tukey, J.W. (1977), Exploratory Data Analysis, Addison-Wesley and Joanes, D.N. & Gill, C.A. (1998), "Comparing measures of sample skewness and kurtosis", The Statistician 47(1), 183-189.
What you can compare
Change one input at a time to see how it affects Count (n), Sum and Mean. The inputs you can vary are Data set, Quartile method and Outlier fence multiplier.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What is the range of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?
On the figures this page opens with, the range is 7. No single number fits everyone: it follows Data set, Quartile method and Outlier fence multiplier, so enter your own above and the answer updates as you type.
What is a formula for range?
Computes the full descriptive summary of a data set: count, sum, mean, median, mode, range, midrange, sample and population variance and standard deviation, quartiles, interquartile range, percentiles. On this page it is computed from Data set, Quartile method and Outlier fence multiplier and shown as Count (n), Sum and Mean.
How do they calculate the range?
Computes the full descriptive summary of a data set: count, sum, mean, median, mode, range, midrange, sample and population variance and standard deviation, quartiles, interquartile range, percentiles. Open “How this is worked out” beside the result to see each step for your own figures.
How to do domain and range?
It needs Data set, Quartile method and Outlier fence multiplier. Nothing else is required, and the figures stay in your browser.
What information do I need for the Range Calculator?
You need Data set, Quartile method and Outlier fence multiplier. The page opens with default figures that give range of 7, so you can see the scale before entering your own.
What does this Range Calculator show?
It shows Count (n), Sum, Mean, Median, Mode, Modal values, Minimum and Maximum, with the working and any warnings for your entries.