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

Concept:
A negatively skewed distribution (also called left-skewed distribution) has a longer tail on the left side. In such distributions, smaller values pull the mean toward the left. Because of this effect:

• The mean is pulled most toward the tail.
• The median lies between the mean and the mode.
• The mode remains near the peak of the distribution.

Thus, the relationship becomes: \[ \text{Mean}<\text{Median}<\text{Mode} \]
Step 1: Understand the effect of skewness.
In a negatively skewed distribution, extreme low values pull the mean toward the left side.
Step 2: Determine the order of central tendencies.
Since the mean is affected the most by extreme values: \[ \text{Mean}<\text{Median}<\text{Mode} \]
Step 3: State the conclusion.
\[ \therefore \text{The correct relationship is Mean }<\text{ Median }<\text{ Mode.
\]