A histogram is titled 'Points Scored per Player from Eastern High School in the Championship Game.' The x-axis ranges from 0 to 11 and the y-axis ranges from 0 to 3, both by 1-unit increments.

A histogram is titled 'Points Scored per Player from Western High School in the Championship Game.' The x-axis ranges from 0 to 17 and the y-axis ranges from 0 to 3, both by 1-unit increments.
Compare the skewed distributions that summarize the number of points scored per player in the championship basketball game between Eastern High School and Western High School. Which statement correctly compares the medians of the two distributions?

(1 point)
Responses

The median for Eastern High School is less than Western High School because they did not have the highest scorer of the game.
The median for Eastern High School is less than Western High School because they did not have the highest scorer of the game.

The two teams have an equal median number of points scored because one data set is skewed right and the other is skewed left.
The two teams have an equal median number of points scored because one data set is skewed right and the other is skewed left.

The median for Eastern High School is several points higher than that of Western High School because the Eastern’s dataset is skewed left.
The median for Eastern High School is several points higher than that of Western High School because the Eastern’s dataset is skewed left.

The median for Western High School is greater than Eastern High School because they played one less player in the game.

1 answer

To compare the median points scored by players from Eastern High School and Western High School based on the given information about their histograms, we should focus on the characteristics of the distributions, particularly how they are skewed and the implications for their medians.

  1. A left skewed distribution (skewed to the left) typically has a median that is higher than the mean, as the long tail is on the left side, pulling the mean down more than the median.
  2. A right skewed distribution (skewed to the right) typically has a median that is less than the mean, as the long tail is on the right side, pulling the mean up more than the median.

Since Eastern High School's histogram suggests a smaller range of points with a peak likely on the lower end (suggestive of being left skewed) and Western's histogram covers a wider range but extends towards higher scores (possibly right skewed), it would be reasonable to conclude that:

  • Eastern High School likely has a higher median due to its left skew.
  • Western High School may have a median that is lower than what one might expect due to its right skew.

However, without specific data points or frequencies to ascertain the exact values of the medians, we can only deduce possible scenarios based on the shape of the distributions described.

Given these insights, the statement that accurately reflects the comparison of medians based on their skew would be:

"The median for Eastern High School is several points higher than that of Western High School because the Eastern’s dataset is skewed left."

This indicates that the left skew of Eastern's distribution contributes to a higher median compared to Western's distribution filled with higher scores.