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Descriptive Statistics · Paper 3 — Free Maths AI HL Practice Questions

1ChallengeLAQMeasures of central tendency (mean, median, mode)9 marksPaper 3~14 min
A large-scale agricultural study investigates the relationship between a new organic fertilizer and crop yield. For 100100 randomly selected farms, the annual yield (in tonnes per hectare) is recorded. Each farm uses either the organic fertilizer (Group A) or a conventional synthetic fertilizer (Group B). - Group A (5050 farms): mean =4.82= 4.82, standard deviation =0.75= 0.75, median =4.90= 4.90, mode =5.10= 5.10 (all in tonnes per hectare) - Group B (5050 farms): mean =4.41= 4.41, standard deviation =0.82= 0.82, median =4.35= 4.35, mode =4.20= 4.20 (all in tonnes per hectare)
(a)
Show that the combined mean yield for all 100100 farms is 4.6154.615 tonnes per hectare. [2 marks]
(b)
Calculate the difference (mean −- median) for Group A and for Group B. [2 marks]
(c)
A researcher claims: "The median is a more representative measure of central tendency than the mean for comparing these two groups, because the mean is sensitive to extreme values." Using your results from part (b) and the concept of skewness, evaluate this claim. [3 marks]
(d)
A new farm, Farm X, which uses the organic fertilizer and has a yield of 6.506.50 tonnes per hectare, is added to Group A. (i) Calculate the new mean of Group A (now 5151 farms). [1]
(ii) Determine the new median of Group A and hence show that the mean increases by more than the median increases. [2 marks]
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Solutions

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