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ELI5 Yahaaa

Count a little, multiply a lot

How Do You Count a Huge Crowd?

Nobody counts a crowd. They count one small patch and multiply by how many patches there are.

1 Count onesquarecarefully2 Count how manysquares thereare3×Multiply — thatis your crowd
Sampling turns an impossible count into two easy ones.
  1. Step 1 of 5

    Counting everyone is impossible.

    Counting each person?Slow, and always wrongCounting a patch Fast, and close

    People move, overlap and leave. Any count that takes an hour is counting a different crowd at the end than at the start.

  2. Step 2 of 5

    So you count one patch properly.

    The whole space One square, countedproperly

    Pick a square you can genuinely count — ten people by ten people — and count it slowly and honestly. That number carries everything.

  3. Step 3 of 5

    Then you count squares instead of people.

    1 Measure thespace2 Divide intosquares3 Count thesquares

    How many of that square fit in the space? That is a measuring job, not a counting job, and it is far easier.

  4. Step 4 of 5

    Multiplying is the whole method.

    1 80 people inone square2×× 150 squares3 About 12,000people

    People per square, times squares, equals people. It is one multiplication standing in for tens of thousands of counts.

  5. Step 5 of 5

    The error comes from the patch you chose.

    A typical square The estimate holds upThe densest square The estimate is far toohigh

    Crowds are thicker at the front and thinner at the edges. Counting one dense square and multiplying gives a badly inflated answer.

    Rival crowd counts at the same event often differ by a factor of three, and the argument is always about which patch was sampled.

The short version

Crowds are counted by counting one honest patch and multiplying by the number of patches, so the choice of patch is everything.

Try it yourself

Estimate the blades of grass in a lawn: count a 10 cm square, then work out how many squares the lawn holds.

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