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Data and graphing

A chart is a way of showing counts so they can be compared at a glance, and every form here does the same job differently. A tally is quick to keep while you are still counting. A pictograph swaps one symbol for several things, which saves space and adds a multiplication. A bar graph reads against a numbered scale. A line graph follows one thing as it changes over time. The skill is the same in all four: find the row, read the number honestly, and answer the question that was actually asked.

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Counting a tally

How many children chose the cat? (a tally chart with four rows; the cat row has two gates of five and two single marks)

  1. Find the cat row and look only at that row.
  2. Count the gates first. Each gate is four marks with one struck across them, so each gate is 5.
  3. Two gates is 5 and 5, which is 10.
  4. Then the loose marks: two more.
  5. 10 and 2 is 12, so 12 children chose the cat.

Worth knowing. The gates are the whole reason a tally is drawn this way. Counting 12 separate strokes is slow and easy to lose; counting 5, 10, then 2 is neither.

Reading a pictograph with a key

How many children chose the apple? (a pictograph where one symbol stands for 5 children; the apple row has 4 symbols)

  1. Read the key first, every time. It says one symbol stands for 5 children.
  2. Count the symbols in the apple row: 4 of them.
  3. So this is 4 lots of 5, not 4.
  4. 4 times 5 is 20, so 20 children chose the apple.

Worth knowing. Answering 4 here is the single most common mistake on a pictograph, and it comes from counting before reading the key. The key is doing all the work.

A scale that does not start at nothing

How many more children chose the melon than the banana? (a bar graph whose scale runs from 40 to 60; melon reads 57 and banana reads 51)

  1. The melon bar looks about twice as long as the banana bar, so it is tempting to say the melon is twice as popular.
  2. Check where the scale starts. It starts at 40, not at nothing, so most of both bars is not drawn at all.
  3. Read the actual numbers off the scale: melon is 57, banana is 51.
  4. 57 take away 51 is 6, so 6 more children chose the melon.

Worth knowing. Nothing on this chart is untrue, and the impression it gives is still wrong. That is exactly why it is worth being able to spot: the defence is to read the numbers rather than the picture.

Where it usually goes wrong

  • Counting symbols on a pictograph instead of reading the key. Four symbols at 5 each is 20, and 4 is the answer to a different question.
  • Assuming a scale starts at zero. If it does not, the bars exaggerate every difference on the chart — check the bottom of the scale before you compare anything.
  • Reading the wrong row. With the labels down one side it is easy to slip a line, so put a finger on the row you want before you start counting.
  • Answering “how many more” with the bigger number instead of the difference. The question asks for the gap between the two, not the size of one.

The Professor reads the numbers up the side of a graph before he looks at the bars. Twice now he has been fooled by a chart that looked dramatic and was not, and he says once was quite enough.

Practise it

All level paths

Questions teachers and parents ask

Why do some of these graphs have a scale that does not start at zero?

Because real ones do, and a child who has never seen it has no defence against it. A scale starting part way up makes a small difference look enormous, which is the most common way an honest-looking chart misleads — in advertising, in news graphics, everywhere. The questions on those levels are still perfectly fair: the scale is numbered, so reading it correctly gives the right answer every time. Only the impression is misleading, and noticing that is the skill being taught.

Why is there no question asking which was most popular?

Because the answer would be a word rather than a number, and a printed answer key has to be markable without argument. "The tallest bar" is easy to see and hard to mark once a child writes "the red one" or "red" or "the third". Asking for the count of the tallest bar tests the same reading and lands a single number in the box. It is worth asking out loud at home, where you can hear the reasoning.

My child can read the bar graph but not the pictograph. Is that normal?

Yes, and it is a good sign about what they are finding hard. A bar graph is reading; a pictograph is reading and then multiplying, and the multiplication is hidden — nothing on the page says "times by five" except the key. If the key is being skipped, cover the symbols and ask what one of them is worth before uncovering them again.

Is the data real?

No, and deliberately so. Every chart on this site is generated from a seed: the categories are invented, the counts are made up, and no real child's survey answers are anywhere near it. That is a privacy decision as much as a practical one — this site collects nothing about anybody, so it has nothing real to plot.

Where this shows up

Standards

  • 1.MD · Measurement and data
  • 2.MD · Measurement and data
  • 3.MD · Measurement and data
  • 4.MD · Measurement and data
  • 5.MD · Measurement and data
  • 6.SP · Statistics and probability
  • CCSS.MATH.CONTENT.1.MD.C.4 — Organise, represent and interpret data with up to three categories, and answer questions about how many in each category and how many more or fewer there are in one than another.
  • CCSS.MATH.CONTENT.2.MD.D.10 — Draw a picture graph and a bar graph to represent a data set with up to four categories, and solve simple put-together, take-apart and compare problems using the information in it.
  • CCSS.MATH.CONTENT.3.MD.B.3 — Draw a scaled picture graph and a scaled bar graph to represent a data set, and solve one- and two-step how many more and how many fewer problems using the information in them.
  • CCSS.MATH.CONTENT.5.G.A.2 — Represent real world problems by graphing points in the first quadrant of the coordinate plane, and interpret what those coordinate values mean in the situation.
  • CCSS.MATH.CONTENT.6.SP.B.5 — Summarise numerical data sets in relation to their context, including the number of observations and what was measured.

Formats