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📊 Primary Maths & Science Games · Grade 4 · Bar charts and the mean

Charts and the Mean: Read It, Draw It, Level It Out

Local Calculation · Private

The usual slips are forgetting what one square stands for, and adding up for the mean without dividing (or dividing by the wrong count). Level the bars out once and the mean makes sense: it is the evened-out value, not necessarily one of the numbers, and it does not mean every value is the same.

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How to play

  1. In Explore, drag bars up or down, set one square to 1, 2 or 5, switch to the pictograph, sort or reset.
  2. Tick Mean to show the mean line (orange is extra, dashed is missing), then press Level out (pause any time) to make the bars equal while the total stays the same.
  3. Levels: pictographs, drawing a bar chart from a table, comparing, finding the mean, and using the mean.

Curriculum unit

Primary maths, grade 4: bar charts with a scale, the mean, and reading and comparing charts (PEP textbook, grade 4 volume 1 unit 7 and volume 2 unit 8).

For parents and teachers

Mistakes are grouped as counting pictures only, the scale, most and least, adding instead of subtracting, forgetting to divide, dividing by the wrong count, giving the mean as the missing value, how the mean moves and the average-depth idea. Worksheet questions give the data in words.

FAQ

How do I find the mean?
Mean = total ÷ how many numbers. Add them all up, then divide by the count. You can also level out: move the extra from big values to small ones until they are all equal.
Is the mean always one of the numbers?
No. It is the evened-out value, so it can differ from every number and can be a decimal, but it always lies between the smallest and the largest.
What does “one square stands for 2” mean on a bar chart?
Each square counts as 2. A bar 5 squares tall shows 10; a bar ending halfway between two lines shows an odd number, like 4½ squares for 9.