If a distribution is negatively skewed, then:Select one:a.mean > median > modeb.mean < median < modec.median > mean > moded.mean = mode = median

Break Down the Problem

1. Interpret the question about the relationship between the mean, median, and mode in a negatively skewed distribution.
2. Identify the characteristics of negatively skewed distributions and how they affect these measures of central tendency.

Relevant Concepts

• In statistics, when a distribution is negatively skewed, it means that the tail on the left side (lower value side) is longer or fatter than the right side.
• The general relationship between the mean, median, and mode for a negatively skewed distribution is as follows:
  • The mean is typically less than the median, which in turn is less than the mode.

Analysis and Detail

1. For a negatively skewed distribution:
   • The tail is stretched more to the left, which pulls the mean down.
   • The median, being the middle value, is less affected by the extreme left values compared to the mean.
   • The mode, being the most frequent value, is usually higher than the median in such distributions.

Given these characteristics, we can conclude that:

• Mean < Median < Mode

Verify and Summarize

• Reviewing the relationships among the mean, median, and mode in a negatively skewed distribution confirms that they follow the order: $\text{Mean} < \text{Median} < \text{Mode}$.

Final Answer

The correct option is: b. mean < median < mode.