Below are the body weights of four women and four men (both measured in lbs.).

Women's body weights: {143, 121, 136, 139}
Men's body weights: {209, 195, 189, 204}

Questions:
1. Which measurement is more extreme: a woman weighing 120 lbs or a man weighing 214 lbs?
2. Which group has more variation in their sample?
3. Which group has more variation in their sample relative to their average?

The man's weight of 214 lbs is more extreme than the woman's weight of 120 lbs when compared to their respective groups. The women's weights have higher variability both from the standard deviation and coefficient of variation, relative to the average.

Explanation:

First, we examine the extremeness of the weights provided. In this case, the extremeness is judged relative to the datasets each weight is coming from. The woman's weight of 120 lbs is just 1 lb below the sample's lower limit, while the man's weight of 214 lbs exceeds the sample's upper limit by 10 lbs. Therefore, in this context, the man's weight of 214 lbs is relatively more extreme.

Next, we evaluate the sample's variability or dispersion by calculating the standard deviation. For the women's weights, the standard deviation is approximately 8.86. For the men's weights, it's approximately 7.93. This indicates that the women's weights have more variability.

Finally, when it comes to variation relative to the average, we calculate the coefficient of variation. The women's group has a coefficient of variation of approximately 6.57, and the men's group has a coefficient of 3.94. Therefore, relative to the average, the women's group still has more variation.

Learn more about Descriptive Statistics here:

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