Question

Which of the condition is satisfied as per the figure given below? 

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

Hint:

To identify skewness relationships quickly:
- Symmetrical: Mean = Median = Mode
- Positively (Right) Skewed: Mean \(>\) Median \(>\) Mode (Mean is pulled to the right tail).
- Negatively (Left) Skewed: Mean \(<\) Median \(<\) Mode (Mean is pulled to the left tail).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The relative positions of the mean, median, and mode reflect the skewness (asymmetry) of a frequency distribution.
In a symmetrical distribution, all three values coincide at the center.
In an asymmetrical (skewed) distribution, they are separated in a predictable order.

Step 2: Detailed Explanation:
The given curve shows a positively skewed (or right-skewed) distribution.
This is characterized by a long, thin tail extending to the right toward higher values.
Let us analyze the positions of the three parameters in this distribution:
- Mode: It corresponds to the highest point (peak) of the curve, representing the value with the highest frequency.
Because the peak is on the left, the mode has the smallest value.
- Mean: It is highly sensitive to extreme values.
The long tail to the right contains extreme high values, which pull the mean significantly to the right (toward the tail).
Therefore, the mean has the largest value in this distribution.
- Median: It divides the total area under the curve into two equal parts.
It is resistant to extreme outliers, so it always lies between the mode and the mean.
Comparing their values on the horizontal axis from left to right:
\[ \text{Mode} < \text{Median} < \text{Mean} \] Which can be written as:
\[ \text{Mean} > \text{Median} > \text{Mode} \] This matches Option (B).

Step 3: Final Answer:
For the given positively skewed distribution, the condition satisfied is Mean \(>\) Median \(>\) Mode.