Question

What does a left-skewed histogram indicate?

• A. The mean is less than the median.
• B. The data is evenly distributed.
• C. The highest frequency is at the right end.
• D. There are no outliers.

Hint:

For skewed distributions, remember the inequality order:
- Left-Skewed: Mean $<$ Median $<$ Mode.
- Right-Skewed: Mode $<$ Median $<$ Mean.
The median is always in the middle.

Answer 1

The Correct Option is A

•

Step 1: Understanding the Question:
The question asks for the statistical implication of a left-skewed (negatively skewed) histogram.
We need to relate the shape of the distribution to the relationship between its mean, median, and mode.

•

Step 2: Key Formula or Approach:
A left-skewed distribution has a long left tail.
Mathematically, for skewed distributions:
- Right-skewed (positive skew): $\text{Mean} > \text{Median} > \text{Mode}$
- Symmetric: $\text{Mean} = \text{Median} = \text{Mode}$
- Left-skewed (negative skew): $\text{Mean} < \text{Median} < \text{Mode}$

•

Step 3: Detailed Explanation:
In a left-skewed histogram, the majority of the data observations are concentrated on the right side of the distribution, with a tail stretching out to the left (towards lower values).
Because the long tail contains extremely low values (outliers on the lower end), these low values pull the mean downwards more than they affect the median.
Consequently, the mean becomes smaller than the median.
The median represents the 50th percentile of the data and remains relatively robust to these extreme low values.
Therefore, a key and definitive mathematical property of a left-skewed distribution is that the mean is less than the median ($\text{Mean} < \text{Median}$).
Option (B) describes a symmetric distribution.
Option (C) says highest frequency is at the right end, which is visually typical but is not the strict mathematical definition of skewness like the mean-median relationship.
Thus, option (A) is the most standard, precise mathematical answer.

•

Step 4: Final Answer:
The correct option is (A), which states that the mean is less than the median.