Question

1. sugar high(er)? researchers collected data on 76 brands of cereal at a local supermarket. for each brand, the values of several variables were recorded, including sugar (grams per serving), calories per serving, and the shelf in the store on which the cereal was located (1 = bottom, 2 = middle, 3 = top). here are parallel dotplots of the data on sugar content by shelf.

a. critics claim that supermarkets tend to put sugary kids cereals on lower shelves, where the kids can see them. do the data from this study support this claim? justify your answer.
b. is the variability in sugar content of the cereals on the three shelves similar or different? justify your answer.

Explanation:

a. To check if the data supports the claim, we look at the dot - plots. The bottom shelf (shelf 1) has a relatively high proportion of cereals with high sugar content. The middle shelf (shelf 2) has fewer cereals with high sugar, and the top shelf (shelf 3) also has fewer cereals with very high sugar compared to the bottom shelf.
b. For variability, we consider the spread of the data points. The bottom shelf has a wide spread (from near 0 to 16 grams of sugar). The middle shelf has a more restricted spread (from near 0 to about 12 grams). The top shelf also has a relatively wide spread but with a different pattern compared to the bottom shelf.

Answer:

a. Yes, the data supports the claim. The bottom shelf (shelf 1) has more cereals with high sugar content (e.g., many dots towards the higher end of the sugar scale) compared to the middle (shelf 2) and top (shelf 3) shelves.
b. Different. The bottom shelf has the most variable sugar content (widest spread of data points), the middle shelf has less variability (narrower spread), and the top shelf has a different pattern of spread compared to the bottom shelf.