Question

In a negatively skewed distribution, what is the correct relationship between the Mean, Median, and Mode?

• A. Mean > Median > Mode
• B. Mean < Median < Mode
• C. Mean \(=\) Median \(=\) Mode
• D. Mode < Median < Mean

Hint:

Remember the order of central tendencies: \[ \text{Negatively skewed: } \text{Mean}<\text{Median}<\text{Mode} \] \[ \text{Positively skewed: } \text{Mean}>\text{Median}>\text{Mode} \] \[ \text{Symmetrical distribution: } \text{Mean} = \text{Median} = \text{Mode} \]

Answer 1

The Correct Option is B

Step 1: Understanding the Question
The question asks for the ordering of the three main measures of central tendency (mean, median, mode) for a negatively skewed (or left-skewed) distribution.
Step 2: Detailed Explanation
Let's understand the concepts:

Mode: The value that occurs most frequently. It corresponds to the peak of the distribution.

Median: The middle value that divides the data into two equal halves. It is less affected by extreme values (outliers).

Mean: The arithmetic average. It is sensitive to extreme values.

In a negatively skewed distribution, the tail of the distribution is longer on the left side. This means there are some extremely low values.

These low values pull the mean to the left, making it the smallest of the three measures.

The median is also pulled to the left but not as much as the mean.

The mode remains at the peak of the distribution, which is to the right of the median and mean.

Therefore, the order from smallest to largest is Mean, then Median, then Mode.
Step 3: Final Answer
The correct relationship in a negatively skewed distribution is Mean < Median < Mode.