5 Number Summary Calculator

Sort the data, then pick out the minimum, the first quartile Q1, the median, the third quartile Q3 and the maximum. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 that gives 2, 4, 5, 7 and 15. Paste your own numbers into the calculator and it does the sorting and splitting for you.

With the exclusive median of halves method, the minimum is 2, Q1 is 4, the median is 5, Q3 is 7 and the maximum is 15. The IQR is 3, the upper fence is 11.5, so 15 is an outlier. This is the default example in the calculator.

Q2 is the median of all the data. Q1 is the median of the lower half and Q3 is the median of the upper half. For the data 1, 3, 5, 7, 9, 11, 13 the median is 7, and with the halves method that leaves out the median, Q1 is 3 and Q3 is 11. Software that interpolates may give slightly different quartiles.

Q1, Q2 and Q3 are the three quartiles that cut sorted data into four equal parts: Q1 is the 25th percentile, Q2 is the median and Q3 is the 75th percentile. Q4 is not a separate cut point. People sometimes use it for the maximum, the top of the fourth quarter of the data. The five number summary lists the minimum, Q1, the median, Q3 and the maximum.

Sort the data and decide on a method. With the halves method you split the list at the median and take the median of each half. With the interpolation methods you compute a position, for QUARTILE.INC it is (n − 1) x p + 1, and blend the two neighbouring values. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15, QUARTILE.INC gives Q1 = 4 and Q3 = 6.75.

A quartile calculator sorts your numbers and returns the three quartiles Q1, Q2 (the median) and Q3. This page does that and also gives the minimum, maximum, IQR, range, mean, outlier fences and a list of outliers. You can switch between four quartile methods and see how the answers compare, which matters because textbooks and software disagree.

Type or paste your numbers into the data box, separated by commas, spaces or new lines, choose a quartile method, and press Calculate. The results show Q1, the median and Q3 right away, with the working in the solution view. The default method is the exclusive median of halves, the one a TI-84 uses, so the answers match most classroom keys.

Yes. Scientific and graphing calculators with statistics modes can do it. On a TI-83 or TI-84 you enter the data in a list and run 1-Var Stats, then scroll down to minX, Q1, Med, Q3 and maxX. Basic four-function calculators cannot. This online calculator needs no list setup, you just paste the numbers.

Press STAT, choose Edit and type your data into L1. Then press STAT, move to CALC, choose 1-Var Stats and enter L1. Scroll down past the mean and standard deviation to see minX, Q1, Med, Q3 and maxX. The TI-83 and TI-84 take the median of each half and leave out the overall median, which matches this page's default method.

Use =MIN(range), =QUARTILE.INC(range,1), =MEDIAN(range), =QUARTILE.INC(range,3) and =MAX(range). QUARTILE.EXC is the alternative that excludes the endpoints. For the twelve test scores on this page, QUARTILE.INC gives Q1 = 67 and Q3 = 84.25. Pick the matching method here to reproduce Excel exactly.

Excel interpolates between values, while most textbooks take the median of each half. For 1, 3, 5, 7, 9, 11, 13 Excel's QUARTILE.INC gives Q1 = 4 and Q3 = 10, the same as the inclusive halves, but QUARTILE.EXC gives 3 and 11. Both are valid. Use whichever your course or software uses.

With an even number of values the median is the mean of the two middle values, and the data splits cleanly into two equal halves with no value left over, so the exclusive and inclusive halves methods agree. For the 10 values 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 the lower half is 2, 2, 4, 4, 5 and the upper half is 5, 6, 7, 9, 15.

The median is the single middle value, and you must decide whether it belongs to the halves. The exclusive method leaves it out and the inclusive method keeps it in both halves. For 1, 3, 5, 7, 9, 11, 13 that gives Q1 = 3, Q3 = 11 when exclusive, and Q1 = 4, Q3 = 10 when inclusive.

Exclusive and inclusive describe whether the median is left out of or kept in the two halves when the number of values is odd. The terms are also used for Excel's QUARTILE.EXC and QUARTILE.INC, which are interpolation formulas rather than halves. When n is even, the two halves methods give identical answers. The names are confusingly shared, so check which kind you mean.

Tukey's hinges are the quartile-like values John Tukey used in his five number summary. They are the medians of the lower and upper halves, with the overall median kept in both halves when n is odd. That is the inclusive halves option here. For 1, 3, 5, 7, 9, 11, 13 the hinges are 4 and 10. R's fivenum function returns them.

The IQR is Q3 minus Q1. Multiply it by 1.5, subtract the result from Q1 for the lower fence and add it to Q3 for the upper fence. Any value outside the fences is an outlier. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15, IQR = 3, the fences are -0.5 and 11.5, and 15 is flagged.

Draw a number line, mark a box from Q1 to Q3 with a line at the median, and extend whiskers to the smallest and largest values inside the fences. Plot anything beyond the fences as separate points. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 the box runs from 4 to 7, the whiskers reach 2 and 9, and 15 is a dot.

No. The five number summary is the minimum, Q1, median, Q3 and maximum. The mean is a separate measure, which this calculator also reports because comparing it with the median hints at skew. For the house prices the median is 247.5 but the mean is 312.9, pulled up by one very expensive sale.

The range is the maximum minus the minimum, so it uses the first and last numbers of the summary. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 it is 15 − 2 = 13. The interquartile range, Q3 minus Q1, is a different and sturdier measure of spread: 3 for the same data.

Yes. The solution view lists the sorted data, the minimum and maximum, how the median was found, the two halves or the interpolation positions behind Q1 and Q3, the IQR and fences, the outliers and the mean. At the end it shows the same data under all four quartile methods. Use the toggle to hide the steps and see only the result.

You need at least two numbers here, and QUARTILE.EXC needs three. The summary is more meaningful with a larger sample: with fewer than about eight values the quartiles jump around from one method to the next. Up to 10,000 values are accepted, separated by commas, spaces, semicolons or new lines.

Compare the distances from the median to Q1 and to Q3, and the whiskers on each side. If the upper part is longer, the data are skewed right. For the house prices the median to Q3 distance is 22.5 while the median to Q1 distance is 15.5, and the maximum sits far above, a right skew.

Worksheets usually follow the TI-84 or textbook rule, the exclusive median of halves. Sort the data, find the median, split into halves without the median when n is odd, and take the median of each half. Check your answer by counting: about a quarter of the values should lie below Q1 and about a quarter above Q3, as with 2, 2, 4, 4, 5, 5, 6, 7, 9, 15.