Question 1
2 marksA student investigated variation in the number of seeds in the pods of broad bean plants growing in a large field. She collected 10 pods from the plants nearest to the gate of the field.
Suggest why her sample might not be representative of the plants in the field. Explain why collecting a larger sample would improve her investigation.
Model answer
The plants near the gate may be different from the rest of the field, for example because people walking through the gate trample them and compact the soil, so the sample is biased; it was not random. A larger sample would reduce the effect of any unusual pods on the mean, so the mean would be more representative of the whole field.
Explanation
A sample is only useful if it represents the population. Sampling from one convenient place introduces bias, which random sampling avoids. Larger samples reduce the effect of chance and anomalous values, so the mean and standard deviation are closer to those of the whole population.
Mark scheme
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1 mark
Plants near the gate may be different, e.g. trampled / growing in compacted soil / getting more light, so the sample is biased OR the sample is not random / not every plant had an equal chance of being chosen
Accept either idea for this mark.
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1 mark
A larger sample reduces the effect of anomalous / extreme values on the mean OR gives a mean closer to the true mean of the population / that is more representative (of the field)
Ignore 'more accurate' or 'more reliable' unless explained. Ignore 'fairer'.