Compare Expected and Observed Counts
Interpret a small sample without treating probability as a quota.
Supplied materials
- Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.
Learn the idea
An expected count is sample size multiplied by a model probability. In the fictional Pp × Pp complete-dominance model, white probability is 1/4 per independent offspring. For 12 offspring, the expected white count is 12 × 1/4 = 3. Expected means the average across many such samples, not a required count in each sample.
A supplied model-simulation record contains 12 outcomes: W, P, P, W, P, W, P, P, W, P, P, P. Here W means white and P means purple. The observed white count is 4, one above the expected 3. That difference does not by itself disprove the model. Larger repeated samples and checking assumptions provide more information; phenotype records alone cannot expose every biological cause.
- Verify the model white probability from a Pp × Pp table.
- Calculate the expected count for 12 outcomes.
- Count W entries and find the observed proportion.
- Explain why observed 4 versus expected 3 is not a logical contradiction.
See the method in action
Expected white count is 3. Observed count is 4, with proportion 4/12 = 1/3. A sample proportion can differ from the model’s 1/4 probability because outcomes vary.
Check your reasoning
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See the answer and explanation
Four whites are possible even though the expected count is three.
Expectation is a long-run average under the model. A particular sample need not match it exactly.
Take it further
Change the sample size to 20 under the same model. Expected white count becomes 20 × 1/4 = 5; the observed count still needs a supplied sample record and is not guaranteed to be five.
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