SKEW

Returns a measure of how skewed a distribution is.

Syntax:

SKEW(number1, number2, ... number30)

number1 to number30 are up to 30 numbers or ranges/arrays containing numbers.

SKEW returns a measure of how skewed a distribution is, relative to a normal distribution - that is, how asymmetric it is. Positive values indicate a distribution with a tail inclining to the positive side, and negative values a distribution with a tail inclining to the negative side. SKEW calculates:

$\frac{n}{(n-1)(n-2)}{\sum }_{i=1}^n(\frac{x_i-\overline{x}}{s}{)}^3$

for the n >= 3 numbers having a standard deviation s > 0.

Example:

SKEW(A1:A30)

returns a measure of how skewed the distribution of numbers in A1:A30 is.

SKEW(1, 3, 4, 5, 9)

returns approximately 0.885, indicating that the tail of this (too small to be useful) distribution inclines to the positive.

SKEW(1, 3, 4, 5, 7)

returns 0; the distribution is symmetric.

Understanding the SKEW Function:

The SKEW function takes a set of numerical data and returns a single value that indicates the asymmetry of the distribution.

• A skew value of 0: Indicates a perfectly symmetrical distribution (like a normal bell curve). The average (mean) and the middle value (median) are equal.
• A positive skew value: Indicates a "right-skewed" distribution. This means the tail of the distribution is longer on the right side. In this scenario, the majority of the data points are on the left (lower end), but there are a few larger values pulling the mean to the right. The mean is typically greater than the median.
• A negative skew value: Indicates a "left-skewed" distribution. The tail of the distribution is longer on the left side. The majority of the data points are on the right (higher end), with a few smaller values pulling the mean to the left. The mean is typically less than the median.

Applying the SKEW Function to the Salary Data:

If we were to calculate the SKEW of the salary data above, the result would be a positive value.

Let's look at why:

• The majority of employees have salaries clustered in the lower to middle range ($45,000 to $85,000).
• However, there are two outliers at the high end: $120,000 and $150,000. These values are significantly higher than the rest of the salaries.

These high salaries pull the average (mean) salary up, making it higher than the median salary (the 8th value, which is $65,000). The SKEW function quantifies this pull, and its positive result tells you that the salary distribution is right-skewed, with a longer tail on the high-salary side.

Conclusion from the SKEW Result:

As an HR manager, a positive skew value for salary data suggests a non-uniform pay structure. It indicates that while most employees earn a similar, more modest wage, there are a few individuals with disproportionately high salaries. This insight is useful for making decisions about compensation fairness, budgeting, and understanding the company's overall financial health.