Question

12, 26, 18, 8, 80, 14, 56, 16
the data above shows the number of points scored by each player on a basketball team during a regional tournament. jennie sampled three of the players and got a mean score of 14. charles sampled three players and got a mean score of 54. explain the difference in the two sample means.

Explanation:

The full dataset has extreme high values (80, 56) and low values (8,12,14). Jennie's sample likely included low-scoring players, while Charles's sample included the two highest-scoring players, leading to very different means due to sampling variability and the presence of outliers in the population data.

Answer:

The difference occurs because the two samples are composed of different players: Jennie's sample likely includes low-scoring players (e.g., 8, 12, 14, whose mean is $\frac{8+12+14}{3}=14$), while Charles's sample includes high-scoring outliers (e.g., 80, 56, and 16, whose mean is $\frac{80+56+16}{3}=54$). The wide range of points in the full dataset allows for drastically different sample means based on which players are selected.