FRQ 2 A group of scientists seek to answer the question: Is there a relationship between brain size and intelligence? A group of 100 volunteers are recruited for study. Each volunteer agrees to have their brain measured and classified as small, medium, or large. They also take an IQ test which classifies them as above or below average intelligence. The table shows the classification of the volunteers.

Brain size

Small

Medium

Large

IQ

Above average

3

29

20

Below average

7

29

12

(a) Calculate the marginal distribution of brain size. Summarize your findings in a sentence.

Here is a mosaic plot of the results of the study.

(b) Describe what this graph reveals about the association between brain size and IQ for the 100 volunteers in the study.

(c)
One year later, the scientists repeat the study using only males. In this study, the distribution of intelligence for those with medium sized brains and the marginal distribution of brain size was the same as the original study. However, in the new study the mosaic plot revealed no association between brain size and IQ for the 100 males in the study. Using the graph provided, sketch the mosaic plot for this new study.