SKEW.P

Calculates a distribution’s skewness using a population data set.

Syntax:

SKEW.P(numberOne, [numberTwo],…)

numberOne, [numberTwo],… are 1 to 255 arguments representing the numbers that you want to use. These arguments can be numbers, cell references or ranges.

Calculation for SKEW.P:

$v = \frac{1}{N} i = 1 \sum N \frac{x _{i} - x ˉ ^{3}}{σ}$

Example:

If numberOne, [numberTwo],… contains 1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,5,5,5,5,5:

SKEW.P(1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,5,5,5,5,5)

returns 0.088130077

If numberOne, [numberTwo],… contains 1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5:

SKEW.P(1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5)

returns 0.008757411

	A	B	C	D
1	1	1	1	0.008757411
2	1	2	2
3	2	2	2
4	3	3	3
5	4	4	4
6	4	5	5
7	5	5	5

Application:

Employee Salary Distribution

Let's imagine you are a data analyst for a company and you want to understand the distribution of salaries across all employees in the marketing department. The company wants to know if the salaries are evenly distributed, or if they are skewed towards lower or higher earners. Since you have the salary data for the entire population of the marketing department, you would use the SKEW.P function.

Salary Data Table (Marketing Department)

	Employee ID	Salary
	A	B
1	101	$60,000.00
2	102	$65,000.00
3	103	$70,000.00
4	104	$75,000.00
5	105	$80,000.00
6	106	$85,000.00
7	107	$90,000.00
8	108	$150,000.00

Applying the SKEW.P Function

You would apply the SKEW.P function to the salary data.

The formula would be: SKEW.P(60000, 65000, 70000, 75000, 80000, 85000, 90000, 150000)

Result and Interpretation

When you calculate this, the SKEW.P function would return a positive value (approximately 1.7256).

What the result means:

Positive Skewness: A positive skewness value (like 1.7256) indicates a "right-skewed" distribution. This means the tail of the distribution is longer on the right side.
Real-world Implication: In this salary example, a positive skewness means that most of the employees have salaries clustered on the lower end, while a smaller number of employees have very high salaries (like the employee earning $150,000). The average salary might be pulled up by these few high earners, but the median salary would be a more accurate representation of what a typical employee earns.

In this scenario, the SKEW.P function provides a clear and objective measure of the salary distribution, showing that it is not symmetrical and is positively skewed. This information can be valuable for making decisions about salary scales, bonuses, and overall compensation fairness within the department.

Result for SKEW.P:

1.7256