Data & Graphs

Depth · one concept from first principles · step 2 of 4

Redraw with one item as the new whole

One graph gives the turnout of an election and another splits the votes cast among candidates. We need one candidate's vote count.
Turnout Voted Did not vote (20%) Share of votes by candidate A B (35%) C (11%) D (5%) Other (4%)
RatiosData & probability
Your answer
How to solve
Strategy Change Focus / Count the Complement — The second graph takes one slice of the first and blows it up into a whole bar. So the chain runs in one direction only: eligible voters, then votes cast, then one candidate's share of those.
1STEP 1

Find the turnout

If 20% did not vote, the rest did.

100 - 20 = 80
2STEP 2

Count the votes cast

Take that share of the five million eligible voters.

5000000 × 0.8 = 4000000
3STEP 3

Find candidate A's share

The vote-share bar covers only the votes cast, and its five sections add to 100%.

100 - 35 - 11 - 5 - 4 = 45
4STEP 4

Apply it to the votes cast

Take 45% of the four million votes -- not of the five million voters.

4000000 × 0.45 = 1800000
Answer
1,800,000 votes
Add the five candidates' votes: 1,800,000 + 1,400,000 + 440,000 + 200,000 + 160,000 comes to 4 million, the votes cast.
Takeaway

When one graph zooms in on a slice of another, its 100% is only that slice.

  • Find the turnout
  • Count the votes cast
  • Find candidate A's share
  • Apply it to the votes cast
Where next?
Another one like thissuggested
12 practice problems
Step back and solidifysuggested
An item's angle out of 360° gives its percentKnowing what 1 cm stands for gives the whole
4 reasoning problems grow out of this type — the bridge toward competition →

A parent dashboard for the family lives at sensimlab.com.

▶ Practice — 12 problems

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