When data is not symmetrical (meaning it's skewed), there's a specific relationship that connects mean, median, and mode.
In symmetrical data, Mean = Median = Mode. However, the question specifies the data is not symmetrical, so this relationship does not apply.
For moderately skewed distributions, the relationship is:
Mode = 3 Median - 2 Mean
This is known as Pearson's empirical relationship.
Consider test scores: 10, 20, 30, 40, 100 (skewed right due to the outlier 100)
Mean = 510+20+30+40+100
Mean = 5200
Mean = 40
Median = 30 (middle value)
Using the formula:
Mode = 3(30)−2(40)
Mode = 90−80
Mode = 10
The other options are incorrect:
Option 1: Median = 3 Mode - 2 Mean has the wrong arrangement
Option 2: Mode = 2 Median - 3 Mean has incorrect coefficients
Option 3: Mode = Median = Mean only applies to symmetrical distributions
Therefore, the correct relationship is Mode = 3 Median - 2 Mean.