Question

The parallel boxplots below display the bag weights of two different brands, a and b, of granola. Which statement best compares the variability of the distributions for the bag weights?

1) The bag weights for brand a are more variable than the bag weights for brand b.
2) The bag weights for brand a have less variability than the bag weights for brand b.
3) The bag weights for brand b are not as spread out as the bag weights for brand a.
4) The bag weights for brand a are higher, on average, than the bag weights for brand b.

Answer 1

Without the specific details of the boxplots, we cannot conclusively say which brand of granola has more variability in bag weights. Variability can be assessed by examining the IQR and whiskers of the boxplots. Also, boxplots show medians, not means, so we cannot compare the average weights of the brands from the boxplots alone.

Step-by-step explanation:

To compare the variability of bag weights for two brands of granola using parallel boxplots, we look at the spread of each plot. Variability can be assessed by examining the interquartile range (IQR), which is the distance between the first quartile (Q1) and the third quartile (Q3), as well as the overall range from the minimum to the maximum values. If Brand A's boxplot shows a larger IQR or longer whiskers than Brand B, then Brand A's bag weights are more variable. Conversely, if Brand B's plot is wider, it indicates greater variability in Brand B's bag weights.

Since the details of the boxplots are not provided in the question, we cannot conclusively decide which brand has more variability. However, a general statement would be: 'If Brand A's IQR and whiskers are wider than Brand B's, then Brand A bag weights have more variability. Alternatively, if Brand B's boxplot is wider, it implies that Brand B has greater variability.' Without specific data, we cannot address statements (1)-(4) accurately.

Furthermore, the mean weight comparison (statement 4) cannot be made from boxplots since they typically show the median, not the mean. To compare means, we would need the actual numerical data.