Question

In a dataset, if the mean is significantly higher than the median, what does it indicate about the distribution?

Hint:

\textbf{Remember:} Mean pulled right → Positive skew. Mean pulled left → Negative skew.

Answer 1

Concept: The relationship between mean and median helps identify the skewness of a data distribution. Skewness indicates whether data is stretched more toward the left or right side. Answer: If the mean is significantly higher than the median, the distribution is positively skewed (right-skewed). Explanation:

In a positively skewed distribution, a few very large values pull the mean toward the right. 
The median remains less affected because it depends on the middle value. 
Therefore: \[ \text{Mean}>\text{Median}>\text{Mode} \quad (\text{usually}) \] 
Characteristics of Positively Skewed Distribution: 

Long tail on the right side 
Presence of high-value outliers 
Common in income distributions, exam scores with few toppers, etc. 
Comparison for Clarity: 

Mean $>$ Median → Positively skewed 
Mean $<$ Median → Negatively skewed 
Mean $\approx$ Median → Symmetrical distribution 
Conclusion: When the mean is much higher than the median, it indicates a positively skewed distribution caused by extreme high values pulling the average upward.