Box Plot Calculator

Choose one data set, two data sets or five numbers. For data, paste the values separated by commas or spaces, pick a quartile method and a whisker rule, and press Calculate. You get the box plot numbers, the fences, the outliers and a text drawing of the plot. The default data 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 gives a box from 4 to 7.

Yes. The solution view lists the sorted data, the five numbers, how the fences were set, which values became outliers and where the whiskers end. It then draws the plot in text on a shared scale and describes what the shape says. Use the button to switch between the full solution and just the result.

It computes the IQR, Q3 minus Q1, then sets the lower fence at Q1 minus 1.5 x IQR and the upper fence at Q3 plus 1.5 x IQR. Any value outside the fences is an outlier and is drawn as a separate point. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 the fences are -0.5 and 11.5, so 15 is flagged.

Select your data, then choose Insert, Charts, Statistics, Box and Whisker. Excel lets you pick Inclusive median or Exclusive median for the quartile calculation in the series options, and show outliers, mean markers and mean lines. To check the numbers behind the chart, run the same data here with the matching method.

Yes. Choose the five numbers option and enter the minimum, Q1, median, Q3 and maximum. The calculator checks they are in order, finds the IQR and fences and tells you if the minimum or maximum would be drawn as an outlier. For 10, 22, 30, 41 and 95 the upper fence is 69.5, so 95 is flagged.

Sort the data and find Q1, the median and Q3. Draw a box from Q1 to Q3 with a line at the median. Extend whiskers to the smallest and largest values inside the fences and plot anything beyond as a dot. For 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 the box runs from 4 to 7 with whiskers to 2 and 9.

Yes. Choose the two data sets option and enter both lists. The text plots are drawn on one shared scale so the boxes line up, and the steps say which set has the higher median and the wider middle half. In the example, Set B has a median of 10 against 5 and an IQR of 8 against 3.

The IQR is the width of the box, Q3 minus Q1. Read Q1 from the left edge of the box and Q3 from the right edge, then subtract. In the example, Q1 is 4 and Q3 is 7, so the IQR is 3. The calculator shows it directly as the interquartile range result.

Q1 is the left edge of the box, the value a quarter of the way up the sorted data. Q2 is the median, the line inside the box. Q3 is the right edge, three quarters of the way up. A quarter of the data lies below Q1, half below Q2 and three quarters below Q3. In the example they are 4, 5 and 7.

Whiskers show the spread of data outside the box. With the usual Tukey rule they reach the smallest and largest values that are still inside the fences. With the minimum and maximum rule they reach the extremes. In the example, the Tukey whiskers end at 2 and 9, while the min and max whiskers end at 2 and 15.

The line inside the box marks the median, the middle value of the sorted data, so half of the values lie on each side of it. Some plots add a separate mark for the mean. If the median line is off-centre in the box, the middle half of the data is skewed toward the longer side.

Look at where the median sits in the box and at the length of the whiskers. A median close to Q1 and a longer upper side mean right skew. A median close to Q3 and a longer lower side mean left skew. The calculator reports (Q3 + Q1 − 2 x median) / IQR, which is 0.333 for the example, right skew.

They are outliers: values more than 1.5 IQR below Q1 or above Q3 with the default setting. They are not errors by definition, just values unusual compared with the rest. In the example, 15 is a dot because the upper fence is 11.5. Change the multiplier to 3 and it falls inside, as the fence table shows.

Quartile methods differ. Textbooks and the TI-84 take the median of each half without the middle value, Tukey hinges keep it in, and Excel interpolates. For 1, 3, 5, 7, 9, 11, 13 the exclusive method gives Q1 = 3 but the inclusive method gives 4. Pick the method your source uses.

A histogram shows the full shape of the data by counting values in bins, so you can see peaks and gaps. A box plot compresses the data to five numbers and outliers, which makes it compact and good for comparing several groups, but it hides how many peaks there are. Use both when the shape matters.

Some box plots add a marker for the mean, but the classic box plot does not. This calculator does not draw the mean on the text plot. You can compare it with the median yourself: in the example the mean is 5.9 and the median is 5, a gap that hints at the high outlier.

At least two here, and three for QUARTILE.EXC. A box plot is more reliable with larger samples. With fewer than about eight values the quartiles change a lot between methods, and one value can move the whole box. Showing the sample size beside the plot is good practice.

A modified box plot is the common kind that stops the whiskers at the fences and draws outliers as separate points, rather than extending the whiskers to the minimum and maximum. This calculator offers both through the whisker rule setting, with Tukey's 1.5 x IQR rule as the default.

Yes. The steps include a plot drawn in text characters and a sentence that describes the shape. In the text plot, a bracket marks each box edge, a bar marks the median and whisker ends, dashes mark whiskers, equals signs fill the box and o marks an outlier. It also works with screen readers. The example plot ends with an o at 15.

Then the left part of the box has no width and the median line sits on the box edge. It happens when many values repeat, as in 2, 2, 2, 3, 5, 8. The plot is still correct. The skewness value will be at its extreme, and if Q1 equals Q3 the IQR is 0 and the shape cannot be read from the quartiles.

Yes. The scale simply extends below zero. Try -30, 10, 11, 12, 13, 14, 15, 16, 17, 40: the quartiles are 11, 13.5 and 16, the whiskers end at 10 and 17, and both -30 and 40 are outliers. Nothing in the method needs positive numbers, only that the data are numeric.

The range-bar method came from Mary Eleanor Spear in 1952. John Tukey introduced the box-and-whisker plot in 1970 and described it in his 1977 book Exploratory Data Analysis, which is why the 1.5 x IQR whisker rule carries his name. The plot is now standard in statistics courses and software.