Question

Data was collected on the heights of boys at 12 and 24 months of age. The data is summarized in the following boxplots. Is there more variation in the boys' heights at 12 months or 24 months? Explain how you can tell from the boxplots.

A. There is more variation in height at 24 months. The whiskers are more symmetric for the​ 24-month data, indicating greater spread in the data.
B. There is more variation in height at 12 months. The box length is​ smaller, indicating a smaller interquartile range and greater spread in the data.
C. There is more variation in height at 12 months. The whiskers are less symmetric for the​ 12-month data, indicating greater spread in the data.
D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data

Answer 1

D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data

Explanation:

One easy way we can easily tell about the spread and variation data sets is by considering the length of the box in the box plot.

The length of a box plot represents the interquartile range of a data set. The longer the box length, the more the variation and spread there is in the data.

Therefore, considering the diagram of the box plots attached below, the box length for length of boys at 24months is longer than that of the box length of heights of boys at 12 months.

The longer box lengths for heights of boys at 24 months indicates a larger interquartile range compared to that of heights of boys at 12 months. This larger interquartile range implies that, there is more variation in heights at 24 months.

Therefore, the correct option is "D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data."