If Q3 - Q2 > Q2 - Q1, the value of Bowley's coefficient of skewness is:
positive
To determine the value of Bowley's coefficient of skewness given the condition Q3 - Q2 > Q2 - Q1, we use the formula for Bowley's coefficient of skewness (Sk):
Sk = (Q3 + Q1 - Q2 - Q2) / (Q3 - Q1)
Where:
- Q3 is the third quartile.
- Q2 is the second quartile (median).
- Q1 is the first quartile.
Given that Q3 - Q2 > Q2 - Q1, we interpret this as the distance from the median to the third quartile being greater than the distance from the first quartile to the median. This implies that Q3 is further from Q2 compared to Q1, indicating a longer upper tail, which results in a positively skewed distribution.
Substituting the inequality into the Bowley's formula:
- The numerator (Q3 + Q1 - 2*Q2) will be positive because Q3 is larger compared to Q1 when the difference with Q2 is greater.
- The denominator (Q3 - Q1) is always positive as Q3 > Q1.
Therefore, Sk > 0, indicating a positive skewness.
In conclusion, if Q3 - Q2 > Q2 - Q1, Bowley's coefficient of skewness is positive.
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