Chart Maker
Venn diagrams, tally charts, dot plots and box-and-whisker plots — built from your data rather than from your answers. Type what you have and the counting is done for you.
Every region
| Region | In words | Count | Members |
|---|---|---|---|
| A − (B ∪ C) | A only | 3 | 1, 2, 3 |
| B − (A ∪ C) | B only | 1 | 8 |
| C − (A ∪ B) | C only | 1 | 9 |
| A ∩ B − C | A and B only | 2 | 4, 5 |
| A ∩ C − B | A and C only | 0 | — |
| B ∩ C − A | B and C only | 1 | 7 |
| A ∩ B ∩ C | In all 3 | 1 | 6 |
Type the data, not the answer
Every Venn diagram maker I could find asks you for the size of each region. You work out that four things are in A only, three are in both and five are in B only — and then it draws those three numbers inside two circles.
But working out those three numbers is the exercise. By the time you can fill in that form you have finished the question, and the tool is a drawing program. The same is true of a tally chart maker that asks for frequencies: counting the raw data is the entire thing a tally chart exists to do.
So this takes the members and the observations. The regions and the frequencies are computed, each region is listed with what is actually in it, and the counts are checked against each other — the region totals have to add up to the size of the union, and you can see that they do.
Reading a Venn diagram
Two circles divide into three regions; three circles divide into seven. Each region is named by which sets it is inside and which it is outside, and the table gives both the notation and the plain English, because questions use one and answers are marked in the other.
| Notation | In words | What it holds |
|---|---|---|
| A − (B ∪ C) | A only | In A, in neither of the others |
| A ∩ B − C | A and B only | In both A and B, but not C |
| A ∩ B ∩ C | In all three | The centre, in every set |
| A ∪ B | In A or B or both | Everything inside either circle |
Note that “or” in set language includes “both”. The union of A and B is everything in either circle, the overlap included, which is not how the word is always used in ordinary speech and is the single most common misreading of these questions.
The empty region is a result
If no member is in A and C but not B, that region shows a zero rather than disappearing. A diagram that drops it makes “we checked and it is empty” look identical to “we did not consider it”, and a good many questions turn on exactly that distinction.
A set holds each member once
That is what makes it a set rather than a list. If you type 3, 3, 5 you have described a set of two members, and this tool drops the repeat and tells you it did — because a count that comes out lower than the number of things you typed is otherwise baffling, and the cause is usually either a typo or data that is genuinely a list.
Members are compared as text with the spaces trimmed, so “cat” and “cat ” are the same member, and “Cat” is a different one. Commas, semicolons and line breaks separate; spaces do not, so “red apple, green pear” is two members rather than four.
Why a tally chart counts in fives
The point of a tally is to be countable at a glance without re-counting from the start. Five is about the largest group most people can take in without counting the marks one by one, and the struck-through gate — four uprights with a diagonal through them — makes each group unmistakable even in a long row.
So the marks here are drawn as gates and a remainder, and the table shows the arithmetic beside them: three gates and two left over is 3 × 5 + 2 = 17. The step from marks to frequency is the step that gets dropped, and dropping it is where the miscount happens.
The marks are drawn rather than typed because the gate has no character of its own. In text it has to be faked with combining strokes, which render differently in every font and break when pasted somewhere else. Drawn as lines it looks the same everywhere and exports as a vector. The text version is in the table for copying.
Tally chart or dot plot?
They carry the same information and are read differently. A tally is for collecting — it is what you draw while the data is arriving, because adding one more mark costs nothing. A dot plot is for looking: the columns have a height you can compare at a glance, so the shape of the distribution, the spread and any outlier are visible immediately.
The usual classroom sequence is to tally while counting and then redraw as a dot plot or a bar chart to read the result. Both tabs here work from the same observations, so you can switch between them without retyping.
Box and whisker: five numbers, several groups, one axis
A box-and-whisker plot compresses a dataset to five numbers — the minimum, the first quartile, the median, the third quartile and the maximum — and draws them so that the middle half of the data is a box and the tails are lines. The box spans the interquartile range, so half of every dataset sits inside it by definition. The heavy line inside the box is the median, and reading a box plot starts there.
The box plot here takes up to four groups and draws them on a single shared axis, one above the other. That is deliberate, and it is the main thing it does differently. Almost every box plot maker online draws one dataset at a time, which means comparing two groups involves two pictures with two independently chosen scales — and two scales make a wider spread look narrower, or a lower median look higher. The question a box plot is set to answer is nearly always comparative: did the second class do better, is this machine more consistent, which supplier varies more. That question needs one axis.
The default example is two classes' marks on the same test. Their medians are close. Their spreads are not, and Class B has a minimum far below anything in Class A. A pair of means would have reported those two classes as nearly identical.
Where the whiskers stop
The whiskers reach the furthest value that is still within 1.5 times the interquartile range of the nearer quartile. Anything beyond that is drawn as its own point and called an outlier. The 1.5 is Tukey's convention rather than a derived constant: for roughly normal data it leaves about 0.7% of values outside, which is rare enough to be worth looking at and common enough not to be alarming.
Note that the whisker stops at a value in the data, not at the fence. On 1, 2, 3, 4, 5, 6, 7, 8, 9, 50 the lower fence sits at −4.5, and nobody measured −4.5 of anything. Drawing the whisker down to the fence is a common error in hand-drawn plots and in a surprising number of tools; it makes the chart claim a reading that does not exist. The table below the chart lists both the fence and the value the whisker actually reaches, so the difference is visible.
Why your calculator and your textbook disagree about Q1
This is the most common question about box plots, and it is not a mistake on anybody's part. There is more than one definition of a quartile, three are in wide use in schools, and they give different answers on the same data.
Take the five values 1, 2, 3, 4, 5. The median is 3. Then:
- Exclusive — split at the median and leave it out of both halves. The lower half is 1, 2, so Q1 = 1.5; the upper half is 4, 5, so Q3 = 4.5. This is what a TI-83 or TI-84 reports, and what Moore & McCabe and most US statistics courses teach.
- Inclusive — the same split, but the median belongs to both halves. The lower half is 1, 2, 3, so Q1 = 2; the upper half is 3, 4, 5, so Q3 = 4. These are Tukey's hinges, and they are standard in many UK and IB textbooks.
- Interpolated — no halves at all. Q1 sits at
position 1 + 0.25(n − 1) through the sorted list, interpolating
between neighbours where that lands between two values. Here that is
position 2, so Q1 = 2. This is what Excel's
QUARTILEandQUARTILE.INCreturn, and R's default.
All three are correct under their own definition. Three different quartiles mean three different interquartile ranges, three different fences and sometimes a different set of outliers — which is how the same ten numbers can have an outlier in one tool and none in another.
Two things are worth knowing. The exclusive and inclusive conventions always agree when n is even, because then there is no middle value to argue about; they can only differ on an odd-sized dataset. The interpolated convention can differ from both whatever n is, and in practice usually does — agreement needs repeated values around the quartile positions, so that interpolating between neighbours has nothing to interpolate.
The quartile selector above the chart switches convention, and whenever the three disagree a table appears showing all three side by side with the one you have chosen highlighted. Pick the one your course uses. If you are checking homework, this table is usually the whole answer to "why does the back of the book say something else".
Box plot or dot plot?
A box plot throws information away on purpose, and that is its value: five numbers per group, so several groups fit on one axis and can be compared at a glance. A dot plot keeps every observation, so you can see a gap, a cluster or a second peak — and a box plot cannot show you any of those. A dataset that is strongly bimodal and one that is evenly spread can produce identical box plots. With fewer than about twenty values per group, a dot plot usually tells you more; with several groups of a hundred, the box plot is the only one that stays readable.
Four mistakes this will catch
- Counting the overlap twice. The union is not the sum of the two set sizes; anything in both has been counted twice. The region totals here add to the union, so the arithmetic is visible.
- Putting a member in the wrong region. Each region lists what is in it, so a member that should be in the centre and is not can be seen rather than deduced.
- Losing a tally mark. The frequency column is counted from the data rather than from the marks, so the two agree by construction.
- Reporting one mode when there are two. Where values tie for most frequent, every one of them is listed.
What it does not do
- Venn diagrams of four or more sets, which cannot be drawn with circles at all — they need ellipses, and the regions stop being where anyone expects them.
- Circles sized in proportion to their sets.
- Bar charts, pie charts and histograms — the statistics calculator draws those from the same kind of data.
- Shading or colouring a chosen region.
- Probability calculations from the regions.
- More than four groups on one box plot, or boxes drawn vertically.
- Grouped or summarised input for the box plot — it needs the individual values, because the quartiles cannot be recovered from a frequency table without assuming how the values sit inside each class.
Questions
Why does it ask for the members instead of the size of each region?
Because working out the size of each region is the exercise. A Venn maker that asks how many things are in A only has already had the question answered for it, and all it is doing is drawing three numbers in three circles. Type the members and the regions are computed — which also means the tool can tell you when your counts do not add up, and it can show you exactly which members landed where.
What does the empty region mean?
That no member is in that combination of sets. It is shown with a zero rather than left out, because "we checked and it is empty" and "we did not consider it" are different statements and a diagram that silently drops the region makes them look the same. A common exam question turns on exactly this: noticing that A ∩ C is empty while A ∩ B is not.
I typed six things but the count says five.
A set holds each member once, so a repeat is dropped. The tool says which entries it found more than once, because that is almost always worth knowing — either you typed something twice by accident, or the data genuinely has duplicates and it is a list rather than a set.
Why are the tally marks drawn rather than typed?
Because the five-bar gate — four uprights with a diagonal struck through them — has no character of its own. Writing it in text means combining characters that render differently in every font and break when pasted. Drawn as lines, it looks the same everywhere and exports as a vector. The text version is still in the table, for copying into a document.
Why count in fives at all?
Because the point of a tally is to be countable at a glance without re-counting. Five is the largest group most people can read without counting the marks individually, and the struck-through gate makes each group unmistakable. The table shows the arithmetic — three gates and two left over is 17 — so the step from marks to frequency is visible rather than assumed.
My calculator says Q1 is 1.5 and my textbook says 2. Which is right?
Both. There are three quartile conventions in common use and they disagree on the same data. On 1, 2, 3, 4, 5 the exclusive convention — the TI-83/84 and Moore & McCabe, which leaves the median out of both halves — gives Q1 = 1.5, while Tukey’s hinges and Excel’s QUARTILE.INC both give 2. The quartile selector switches between them, and whenever they disagree a table shows all three side by side. Use whichever your course uses.
Why does the whisker not reach the fence?
Because the whisker marks a value that exists in the data, and the fence is just a boundary calculated from the quartiles. On 1, 2, 3, 4, 5, 6, 7, 8, 9, 50 the lower fence is at −4.5, and nothing was measured at −4.5. The whisker stops at 1, the lowest actual reading inside the fence. A chart drawn down to the fence claims a reading that does not exist, which is a common error in hand-drawn box plots.
Can I compare two or three groups on the same chart?
Yes, and that is what the box plot tab is built for: up to four groups, all drawn on one shared axis. Comparing groups on separate charts with separately chosen scales is how a wider spread ends up looking narrower than it is. The five-number summary table lists every group together for the same reason.
Can I download the chart?
Yes, as SVG or PNG, and both are produced in your browser. The SVG is a true vector file: it stays sharp at any size, prints cleanly, and can be recoloured in Illustrator, Inkscape, Word or LaTeX. Nothing is uploaded anywhere to make it.