Purpose

Return value

Syntax

=SKEW.P(number1,[number2],...)
  • number1 - A range or reference that contains numeric values.
  • number2 - [optional] A range or reference that contains numeric values.

Using the SKEW.P function

The SKEW.P function returns the “skewness” of a distribution. SKEW.P measures the symmetry of a distribution. A positive skew result indicates a distribution that tails off to the right. A negative skew result indicates a distribution that tails off to the left. In a perfectly symmetrical distribution, the skew is zero.

Example

In the example shown, there are 11 numeric values in two groups, A and B. The count of values in each group are the inverse of each other. There are four 1’s in group A, four 5’s in group B, etc. The formula in cell F12 returns a positive skew:

=SKEW.P(B5:B15) // returns 0.7658

The formula in J12 returns a negative skew:

=SKEW.P(C5:C15) // returns -0.7658

Excel also contains the SKEW function , which measures sample skewness. The difference in calculation is related to an adjustment (n-1) made when data represents a sample versus the entire population. More details here .

Purpose

Return value

Syntax

=SLOPE(known_ys,known_xs)
  • known_ys - An array or range of numeric data points (dependent values).
  • known_xs - An array or range of numeric data points (independent values).

Using the SLOPE function

The SLOPE function returns the slope of a regression line based on known y values and known x values. A regression line is a “best fit” line based on known data points.

The slope of a line is a measure of steepness. Mathematically, slope is calculated as “rise over run”, or change in y over the change in x. For example, if a line has a slope of 2/1 (2), then if y increases by 2 units, x increases by 1 unit.

Example

In the example shown, the formula in E5 is:

=SLOPE(B5:B9,C5:C9) // returns -2

This formula returns -2, based on known_ys in C5:C9, and known_xs in B5:B9.

Equation

In statistics, a best fit line does not normally lie exactly on the known x and y points. The equation used by the SLOPE function in Excel is based on the mean of known x’s and y’s:

For the example shown, this formula can be manually recreated like this:

=SUM((B5:B9-AVERAGE(B5:B9))*(C5:C9-AVERAGE(C5:C9)))/SUM((B5:B9-AVERAGE(B5:B9))^2)

The calculated result from the SLOPE function and the manual formula are the same.

Notes

  • If there is only one set of points, SLOPE will return #DIV/0!
  • If the count of known_ys is different from known_xs , SLOPE returns #N/A