Biology by Bradford
cramly
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A simulation to rehearse it, a field notebook to do it, and everything you need to run random quadrat sampling, standard deviation included.
C4.1.3 is Random quadrat sampling to estimate population size for sessile organisms, for both SL and HL. In summary:
The sim makes that last point visible: three populations can have similar means yet very different SDs, and the SD is the only clue students get about the pattern until they reveal the site. The SD vs √mean gauge in both resources is labelled as beyond the syllabus: a hint, not something students must learn.
Hook. Show the "same mean, different SD" figure (sim section 1). Ask: how could you tell these patterns apart if you could only see a few squares?
Sample. Pairs throw 20 random quadrats at each site. Then place 5 by eye on the dandelion meadow and compare the estimates.
Calculate. Students copy the counts into their calculators and check they get the same mean and SD as the sim.
Diagnose & reveal. Each pair commits to even / random / clumped for every site using only their SDs, then reveals. Discuss the error-bar comparison chart.
Plan. Start section 1 of the field notebook for your real site.
Set up. Mark the site with two tapes at right angles. Agree what counts as one individual and the rule for edge cases.
Sample. Groups of 3: navigator (finds coordinates), counter, recorder. Rotate roles. Minimum 10 quadrats per group; pool class data for 30+.
Before leaving. Every group exports or copies its CSV; data stays on the device until it's exported.
Calculate. Mean and SD by calculator, population estimate by hand; check both against the notebook.
Compare. Pool group data. Compare group means and SDs: did bigger samples give more consistent estimates?
Interpret & evaluate. What does the SD suggest about the spread? Sources of error: edge counting, identification, trampling, sample size.
| Challenge | What students should discover |
|---|---|
| Throw 5 random quadrats, then 5 more, then 10 more, and watch the running estimate. | Small samples swing wildly; the estimate settles as n rises. More quadrats = a more reliable mean. |
| Watch the SD while adding quadrats. | The SD doesn't shrink towards zero; it settles on the real variation between quadrats. |
| Place 5 quadrats by eye on the meadow. | Eyes gravitate to visible patches (or to empty-looking spots). The by-eye mean is biased. |
| Sample the barnacle rock with only 5 quadrats. | Clumped populations give the least reliable estimates: one quadrat in a patch changes everything. |
| Compare the desert and meadow SDs. | Similar means, very different SDs: even spacing gives almost identical counts in every quadrat. |
| Hit "New sites" and repeat. | Numbers change, patterns don't. The biology drives the SD. |
Each site is a 20 × 20 grid of possible quadrat positions, so every estimate is mean × 400, but the real-world scales differ (1 m, 10 cm and 10 m quadrats), which is a useful point about matching quadrat size to the organism.
Look for something sessile, easy to identify, with clearly separate individuals, at densities of roughly 1–20 per quadrat.
| Organism | Where | Quadrat | Watch out for |
|---|---|---|---|
| Daisies, dandelions, plantains | Unmown or rough grass | 0.25–1 m² | Count rosettes, not flowers: one plant can have several heads. |
| Clover, buttercups | Field margins | 0.25 m² | Spread by runners: deciding what's "one individual" is a good discussion. |
| Moss cushions, lichen patches | Walls, paths, tree bases | 10 × 10 cm | Agree a minimum size to count. |
| Limpets, barnacles, anemones | Rocky shore | 10 × 10 cm – 0.25 m² | Tide times and footing; barnacles are dense, so use small quadrats. |
| Tree seedlings | Woodland floor | 1 m² | Identification of young seedlings. |
STDEV.S. Worth checking on your department's calculators before the lesson.It's haphazard: throw strength, direction and where you stand all bias it. Random numbers as coordinates are the standard.
Random coordinates can cluster by chance. Evenly spaced placement is systematic sampling, a different method.
The SD reflects real variation in the population. Clumped organisms give large SDs even with perfect technique.
It makes the mean more reliable; the SD settles at the population's true variation rather than falling.
Mark a 2 m × 2 m area of floor with masking tape and scatter three "populations" of small objects: dried beans tossed randomly, rice in tight piles (clumped), and counters placed at regular spacing (even). Students use the field notebook's coordinate generator with a 20 cm quadrat (a card frame works) and collect real data they can analyse in exactly the same way. It's a great rehearsal, but it's no substitute for counting living organisms.