Too many to count? Throw random quadrats, estimate the population, then let the standard deviation tell you how the organisms are spread.
01 · The idea
Count a little, estimate a lot
Random coordinates remove bias.Random numbers decide where each quadrat goes, not your eye, which drifts to the interesting patches.
Scale the mean up.Population ≈ mean per quadrat × (area of site ÷ area of one quadrat).
The SD shows the spread.A small standard deviation means counts are similar in every quadrat: an even spread. A large one means patches and gaps.
Same 48 individuals, same mean of 3 per quadrat: three very different standard deviations.
02 · Into the field
Throw your quadrats
Pick a site. You can only see what's inside a quadrat once you've sampled it. Just like the real thing, you'll never count everything. Roll random coordinates, or switch to place by eye to see what bias does.
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Placement
View
Roll some random coordinates to begin.
Random numbers
x -- · y --
coordinates 00–19 along each tape
Quadrat view
No quadrat yet.
03 · Crunch the numbers
Mean, SD, estimate
Statistics for the site you're on. Random and by-eye quadrats are kept separate so you can compare them.
Counts per quadrat (random only). Shaded band = mean ± 1 SD.How the estimate settles as you add random quadrats.
The data & the formula (you don't need to memorise it)
s = √( Σ(x − x̄)² ⁄ (n − 1) )
In class, use your calculator's statistics mode or a spreadsheet: =STDEV.S(range). Copy these counts in and check you get the same SD as the sim.
04 · Read the spread
Even, random or clumped?
Using only your standard deviations, decide how each population is spread. Then reveal the whole site and the true population.
Going further: SD vs √mean (beyond the syllabus)
When individuals are scattered at random, the SD of quadrat counts comes out close to the square root of the mean. Much smaller than √mean suggests an even spread; much larger suggests clumping. Each card above shows where your data sits on that scale; use it as a hint, not a rule, especially with few quadrats.
Compare the sites
Mean ± 1 SD from random quadrats. Longer error bars relative to the bar = more variation between quadrats = a less even spread.
Biology by Bradford
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