Distribution Mode vs. Mean Relationship

This question asks about the relationship between the Mode and the Mean in a specific type of statistical distribution. Let's explore how these measures behave in different distributions, particularly focusing on skewness.

Understanding Skewness in Distributions

Skewness refers to the asymmetry of a probability distribution. It tells us whether the data is concentrated on one side or if the tail on one side is longer or fatter than the other.

1. Symmetric Distributions

In a perfectly symmetric distribution, the Mean, Median, and Mode are all equal. The data is evenly distributed around the center.

• Mean = Median = Mode

The Normal distribution is a classic example of a symmetric distribution.

2. Positively Skewed Distributions (Right-Skewed)

In a positively skewed distribution, the tail on the right side is longer or fatter than the left side. Most of the data are concentrated on the left side. In this case, the Mean is pulled towards the longer tail (the higher values).

• Mode < Median < Mean

Here, the Mode is the lowest, and the Mean is the highest among the three measures.

3. Negatively Skewed Distributions (Left-Skewed)

In a negatively skewed distribution, the tail on the left side is longer or fatter than the right side. Most of the data are concentrated on the right side. The Mean is pulled towards the longer (left) tail (the lower values).

• Mean < Median < Mode

In this scenario, the Mode is the highest value, followed by the Median, and then the Mean is the lowest.

Answering the Question

The question states that the Mode is found to be higher than the Mean.

Based on our understanding of skewness:

• In symmetric distributions: Mode = Mean.
• In positively skewed distributions: Mode < Mean.
• In negatively skewed distributions: Mode > Mean.

Therefore, the condition where the Mode is higher than the Mean specifically characterizes a Negatively skewed distribution.