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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 —that is yourcrowd
Sampling turns an impossible count into two easy ones.
  1. Step 1 of 5

    Counting everyone is impossible.

    Counting each person?Slow, and alwayswrongCounting 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.

    80 people in onesquare About 12,000 inthe whole spaceOne multiplication, standing in for 12,000 counts

    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.

    The square you happenedto pickPacked tight at the frontThin around the edges
    One badly chosen square, multiplied by 150, is how crowd counts end up in court.

    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

Any count that takes an hour is counting a different crowd by the end, which is why one square is counted and the rest is measured. All the error lives in that square: crowds thicken at the front, and a dense patch multiplied up inflates 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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