Line Plots and Dot Plots

The idea in one sentence

A line plot is a number line with one mark stacked above each measurement, so the numbers you collected turn into a picture of where they piled up.

Building one

Say eight children measured their pencils to the nearest centimetre and got:

Draw a number line that covers every value you have, from 12 to 18, and mark every whole number in between even if nobody got it. Then go through the list once, putting an × above the right number each time.

                    ×
              ×     ×
        ×     ×     ×     ×                       ×
   ─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────
       12    13    14    15    16    17    18

Cross each number off your list as you plot it. Eight measurements means eight marks — counting them at the end is the check that nothing was missed or doubled.

Reading it back

Once it is drawn, four things fall straight out of the picture without any arithmetic.

• The most common value is the tallest stack. Here it is 14 cm, with three pencils.
• The range is the distance from the leftmost mark to the rightmost: \(18 - 12 = 6\) cm.
• The clusters are where the marks bunch up. Most pencils sit between 12 and 15.
• The gaps and outliers are the lonely marks. The 18 cm pencil is well away from the rest — probably a new one, while the others have been sharpened down.

That last one is the real reason to draw a line plot. A list of eight numbers hides an odd one out. A picture makes it obvious.

Line plot, dot plot, bar graph

Line plot and dot plot are the same thing with different marks — some books use ×, others use dots. Nothing else about them differs.

A bar graph looks similar but is not. Bars count categories — favourite fruit, eye colour — and can be shuffled into any order without losing meaning. A line plot sits on a number line, so the order is fixed and the spacing means something. The gap at 16 and 17 on our plot is information; there is no such thing as a gap between “apple” and “banana”.

That is why line plots keep every number in the range, even the empty ones. Leaving out 16 and 17 would squash the picture and hide the outlier.

Fractions on a line plot

By fourth grade the measurements stop being whole. Measure to the nearest quarter inch and your number line is marked in quarters:

Everything else works the same way. One mark per measurement, stacked above the right tick — you just need fractions on a number line to find the tick.

Common mix-ups

• Skipping empty values. If no pencil measured 16 cm, 16 still gets a place on the line. Leaving it out changes the shape of the data.
• Counting stacks instead of marks. Four stacks does not mean four measurements. Add up the marks.
• Unequal spacing. The ticks must be evenly spaced or distances lie.
• Reading the tallest stack as the total. The tallest stack tells you the most common value, not how much data there is.

Check yourself

A line plot has 3 marks above 4, 5 marks above 5, and 1 mark above 9. How many measurements are there, which value is most common, and what is the range?

Marks, not stacks: \(3 + 5 + 1 = 9\) measurements. The tallest stack is above 5, so 5 is the most common. The range runs from 4 to 9, which is 5 — and the lone mark at 9 is an outlier worth asking about.