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Read the chart honestly

Bars that start at 40, "up 5%" that means 5 points, a bigger share of a smaller town: say what a chart really supports, from its numbers.

  • Number sense
  • Untimed
  • Endless levels

How it plays

A small chart drawn in ■ bars, with its axis start stated, or a pair of figures. Say what it honestly supports: the true ratio of two bars, which statement holds, how a change in a percentage should be described, where there are really more people.

Levels go from the true ratio behind bars on a truncated axis, to choosing the honest statement, to percentage points against per cent, rates against counts, and pictures scaled in two directions, which the eye reads by area.

Every chart is drawn from numbers the game chose first, so the true value is known exactly. The wrong options are what the picture suggests, or the classic slips: the bar lengths read as values, the percentage of the wrong base, points called per cent.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This makes reading simple charts and percentage claims more accurately quicker and surer. It claims nothing wider.

Learn

How to get better at read the chart honestly: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read the caption before the bars. “The axis starts at 100” means every bar is missing 100, and the picture is no longer a fair one.
  2. Ignore the lengths of the ■ bars and use the numbers printed at their ends. Those are the data; the bars are only a drawing of them.
  3. Name the base before you compute any per cent: “more than East” divides by East. “Up from 20%” divides by 20.
  4. Work the answer from the numbers, then check that the option you pick says it the same way — times, per cent or percentage points.

Techniques and tricks

  • Add back the missing start

    A bar drawn from a truncated axis shows its value minus the start. To compare two bars, compare the printed values, never the counts of ■.

    e.g. Axis from 100, bars 130 and 145: 145 ÷ 130 = 1.12×. The bars, 6 and 9 squares long, look 1.50×.

  • Per cent more means divide by the smaller

    “A is x% more than B” is (A − B) ÷ B. Dividing by A instead answers a different question: how much less B is than A.

    e.g. South 52, East 40: 12 ÷ 40 = 30% more. 12 ÷ 52 ≈ 23% is how much less East is.

  • Points for the gap, per cent for the growth

    Two percentages differ by percentage points. The change in the rate itself is that gap divided by where it started.

    e.g. 20% to 25% is up 5 percentage points, and 5 ÷ 20 = 25% higher. “Up 5%” would mean 21%.

  • Turn a rate into a count

    A share says nothing about how many people until you multiply it by the size of the group. Do both multiplications, then compare.

    e.g. Town A: 35% of 800 = 280. Town B: 25% of 1,200 = 300. B has more cyclists, at a lower share.

  • Square the scale for a picture

    A picture drawn k times as wide and k times as tall covers k² times the area, and the eye reads area. The figure it stands for only grew k times.

    e.g. Last year 40, drawn 2.5 times as wide and tall: the figure is 40 × 2.5 = 100, but the picture looks 2.5² = 6.25 times bigger.

  • Divide with friendly fractions

    Ratios to two decimal places come quickly if you split them: whole part first, then the remainder as a fraction you know.

    e.g. 38 ÷ 28 = 1 + 10/28 ≈ 1 + 0.36 = 1.36

As the levels climb

  • You start with the true ratio of two bars on a truncated axis. Train the one habit that matters here: eyes to the printed numbers, never to the ■.
  • Next comes “Which statement holds”: three bars and statements in times and per cent. Find the smallest and largest bars, work out (large − small) ÷ small, and match it.
  • Then “Points against per cent” and “Rates against counts” arrive together. For the first, say the gap in points and the growth in per cent separately. For the second, multiply both shares out before you choose.
  • “Pictures scaled by area” comes last. Decide first whether the question asks for the figure (× k) or the look (× k²).
  • Once every kind is open, the questions stop changing and the clock tightens instead, down to half the time. The axis start can also climb higher, which stretches the bars further from the truth, so trust the numbers even more.

Traps to avoid

  • The bar lengths read as values. On an axis that starts above zero, the drawn ratio is always bigger than the true one, and it is usually among the options.
  • The ratio upside down. A choice below 1× when the question asks how many times the bigger one is the smaller is a flipped division.
  • The wrong base for a per cent: dividing the gap by the larger value, or a percentage change by the new rate instead of the old one.
  • Points called per cent. “Up 5%” for 20% to 25% sounds right and is wrong; the game keeps offering it, beside “up 25 percentage points”.
  • A higher share read as more people, or a picture’s area read as its figure. Both are the eye answering before the arithmetic does.

How to practise

  • Open “Kinds of question” and practise one kind at a time while it is new — “Points against per cent” on its own is a good first drill.
  • Switch “Answer by” to “Typing the answer” once you are choosing well: typed, the true ratio and the pictures have no drawn ratio sitting in the options to tempt you, so you have to compute it. The other kinds stay as choices.
  • Turn “Options shown” up towards 8 to see every classic slip side by side. Naming which mistake makes each wrong option is the fastest way to stop making them.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More number sense

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