Three companies (company A, Company B, and Company C) are asked to supply a specific type of concrete for a project and are requested to submit results from a trial batches of that mix which were tested for compressive strength. The distribution of compressive strength tests for each of the three companies are shown below. Which of the following is a TRUE statement?

Question

BlackTom AI · Accepted Answer

Begin by identifying what the question asks: which statement about variability among the three companies is true based on the shown distributions of compressive strength.
Option 1: 'Company C has more variability than either Company A or B.' In the plot, the distribution for C appears the widest spread, indicating greater variability (highest standard deviation) compared to A and B, whose curves are visibly narrower. This aligns with the concept that a broader curve corresponds to more dispersion in the data.
Option 2: 'Company A has more variability than either Company B or C.' This would require A's curve to be the broadest. However, A’s curve is notably narrower than both B and C, indicating less variability, not more. Thus this statement is inaccurate.
Option 3: 'Company B a lower coefficient of variation than the other two companies.' The coefficient of variation (CV) is the ratio of standard deviation to the mean. While B’s curve is moderately spread, CV depends on both spread and center; without exact numerical values, we cannot conclude B has the lowest CV relative to both A and C. Given that C is widest and its mean appears quite lower than A’s, CV could be comparable or even higher. This statement is not reliably supported by the visual data alone.
Option 4: 'Company A has a larger standard deviation than either Company B or C.' A larger standard deviation would require A to be the widest curve, which is not the case here; A is the narrowest among the three. Therefore this claim is incorrect.

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