Dot Plot Maker

How to make a dot plot

1. Paste your values into Set A. A column copied from a spreadsheet works, and so do measurements written as fractions: 1 1/4, 1 1/2, 1 1/2, 2.
2. Leave Step empty and the maker picks one from your data (quarters give a step of 1/4, whole numbers a step of 1), or type the step your worksheet asks for, such as 1/8 or 5.
3. Pick dots or X's, give the plot a title and an axis label, and read the mean, median and mode off the marks, with the range and IQR written underneath.
4. To compare two groups, paste the second into Set B. It is drawn below the same line, or on a second line with the same scale, so stacks at the same value sit straight above each other.
5. Download a PNG or SVG, print the plot, or make a worksheet for practice.

Fractions on a line plot

US grade 4 and 5 standards (4.MD.4, 5.MD.2) ask for line plots of measurements in halves, quarters and eighths of a unit. The step should equal the smallest piece in the data so every value lands on a tick: measurements to the nearest eighth of an inch need a step of 1/8, giving ticks 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1. With Simplify on, 2/8 is labelled 1/4 and 4/8 is labelled 1/2; turn it off if your class labels every tick in eighths. Past 1, ticks are written as mixed numbers (1 1/4) unless you choose plain fractions (5/4) or decimals (1.25).

Values are kept as exact fractions, so 1 1/2, 3/2 and 1.5 are one value and stack in one column. A value that falls between ticks (1/3 on a line of quarters) is drawn at its exact place, and the page tells you how many did.

Reading mean, median and mode from a dot plot

The mode is the tallest stack; if every value appears once, or every stack is the same height, there is no mode, and the page says so. The median is the middle dot counted from the left: 15 dots put it at the 8th, 16 dots halfway between the 8th and the 9th. The mean is the total divided by the count. The range is largest minus smallest, and the IQR is Q3 minus Q1. Quartiles have more than one textbook definition, so the method is named under the plot and you can switch it: the default, median of halves with the median left out, is the one TI-83/84 calculators and most school books use. These are the same four methods, giving the same numbers, as the box plot maker.

A worked example

The example data are 15 bean plant heights in inches: 2 1/4, 2 1/2, 2 1/2, 2 3/4, 2 3/4, 2 3/4, 3, 3, 3, 3, 3 1/4, 3 1/4, 3 1/2, 3 3/4, 4. The tallest stack is four dots over 3, so the mode is 3. Fifteen values put the median at the 8th, which is also 3. They add up to 45 1/4, so the mean is 45 1/4 ÷ 15 = 3 1/60, about 3.02, just right of the median. The range is 4 − 2 1/4 = 1 3/4. With the median left out, the lower half (the first 7 values) has median 2 3/4 and the upper half has median 3 1/4, so the IQR is 3 1/4 − 2 3/4 = 1/2.

What it cannot do

• More than 500 values in a set: only the first 500 are drawn, and the page says so. Stacks over about 30 dots get squeezed (the spacing stays even, the dots get smaller).
• A third data set: two sets is the most one plot holds. Make a second plot for more groups, or use the box plot maker, which takes up to 12.
• No binning into classes. Every distinct value gets its own column, so 40 different decimals make 40 thin columns; for grouped data use the histogram maker.
• Steps that need more than 200 ticks for your data are refused and an automatic step is used instead.
• It does not mark a child's worksheet answers; the answer key is a separate page to check against.
• The PNG and SVG use the fonts on the device that opens them (Geist where it is installed, otherwise Helvetica or Arial).

Privacy and what is stored

Your values never leave your device: the plot, the statistics and the worksheet are worked out and drawn by code in this page, and downloads are made in the browser. Once you edit, the data and settings are saved in this browser's local storage so a reload keeps them; Clear saved data deletes them in one tap. The page sends an anonymous page-view count and, at most, two fixed words (dotplot-make, dotplot-export), never a value or a title. The worksheet seed comes from your browser's cryptographic random generator.

Questions

What is the difference between a dot plot and a line plot?

In US school maths they are the same picture: a number line with one dot or X stacked above it for every data value. Grades 2 to 5 usually call it a line plot and draw X's; grade 6 and statistics books call it a dot plot and draw dots. A line graph, which joins points with lines, is something else.

How do you put fractions on a line plot?

Choose a step equal to the smallest fraction in the data, such as 1/8 for measurements to the nearest eighth of an inch, so every value lands on a tick. Label the ticks 0, 1/8, 1/4, 3/8, 1/2 and so on; with simplify on, 2/8 is written 1/4 and 4/8 is written 1/2. Type the step into Step and the maker draws and labels the line for you. To draw just the line, with points or jumps, use the number line generator.

How do you find the mean, median and mode from a dot plot?

The mode is the value with the tallest stack. The median is the middle dot when you count from the left: with 15 dots it is the 8th, with 16 it is halfway between the 8th and 9th. The mean is the sum of all values divided by how many there are, so a stack of 3 dots over 2 1/2 adds 7 1/2. The maker marks all three on the plot.

How do you compare two dot plots?

Draw both on the same scale and compare centre and spread: which set has the larger median or mean, and which has the larger range or IQR. Paste a second set into Set B and the maker draws it below the line (or on its own line with the same scale), with both sets' mean, median, range and IQR written out. For larger sets of whole numbers a stem and leaf plot keeps every value readable.