Questions: If a distribution of scores has many, many more low scores than high scores, this distribution is best described as . . . Positively skewed Negatively skewed Normal Cannot determine from the information given

Solution Steps

To determine the skewness of a distribution, we need to understand the relationship between the mean, median, and mode. A distribution with many more low scores than high scores is typically positively skewed, meaning the tail on the right side of the distribution is longer or fatter than the left side.

Skewness in a distribution refers to the asymmetry of the distribution of values. A distribution can be:

• Positively skewed: This occurs when there are more low scores and the tail on the right side (higher scores) is longer or fatter. The mean is typically greater than the median in a positively skewed distribution.
• Negatively skewed: This occurs when there are more high scores and the tail on the left side (lower scores) is longer or fatter. The mean is typically less than the median in a negatively skewed distribution.
• Normal: This is a symmetric distribution where the mean, median, and mode are all equal.
• Cannot determine: This option is used when there is insufficient information to determine the skewness.

The problem states that the distribution has "many, many more low scores than high scores." This suggests that the distribution has a longer tail on the right side, as there are fewer high scores compared to low scores.

Based on the analysis, the distribution is likely to be positively skewed because it has more low scores and fewer high scores, resulting in a longer right tail.

Final Answer