Question

1. more olympics athletes who participate in the shot put, discus throw, and hammer throw tend to have different physical characteristics than other track and field athletes. the scatterplot shown here enhances the scatterplot from exercise 5 by plotting these athletes with blue squares. how are the relationships between height and weight the same for the two groups of athletes? how are the relationships different?

Explanation:

To determine the similarities and differences in the height - weight relationships for the two groups of athletes (shot put, discus throw, hammer throw athletes - blue squares; other track and field athletes - black dots):

Similarities:

• Direction of Association: Both groups show a positive association between height and weight. As height increases, weight also tends to increase for both groups. This is evident from the general upward trend of both the blue square (shot put - related athletes) and black dot (other track and field athletes) data points in the scatterplot.
• Form of Association: The relationship appears to be roughly linear for both groups. The points seem to cluster around an imaginary straight - line trend, indicating a linear relationship between height and weight in both cases.

Differences:

• Strength of Association (Spread): The blue square points (shot put - related athletes) are more spread out vertically (in terms of weight) for a given height compared to the black dot points (other track and field athletes). This means that for the same height, the weight of shot put - related athletes has a wider range of values. For example, at a height of around 70 inches, the black dots (other athletes) have weights concentrated in a narrower band (say between 150 - 200 lbs), while the blue squares (shot put - related) have weights ranging from around 200 - 300 lbs.
• Average Weight at a Given Height: For a given height, the shot put - related athletes (blue squares) tend to have a higher weight on average than the other track and field athletes (black dots). For instance, at a height of 74 inches, the black dots are mostly around 150 - 200 lbs, while the blue squares are around 200 - 300 lbs. Also, the shot put - related athletes have a broader range of heights and weights, with some of them being much taller and heavier (e.g., the blue square at height ~82 inches and weight ~350 lbs) compared to the other group.

Answer:

Similarities:

1. Both groups have a positive, linear relationship between height and weight (as height increases, weight tends to increase, and the relationship is roughly linear).

Differences:

1. The shot - put - related athletes (blue squares) have a wider spread of weights at a given height (more variability in weight for the same height) and tend to have a higher average weight at a given height compared to the other track and field athletes (black dots). Also, the shot - put - related group includes athletes with greater heights and weights (e.g., very tall and heavy outliers) that are not present in the other group.