## How to use the SKEW function

**What is the SKEW function?**

The SKEW function calculatesĀ the skewness of a group of values with an asymmetric tail from its mean value.

**What is skewness?**

Skewness and asymmetric tails describe the lack of balance and symmetry in probability distributions and datasets. Identifying skewness is fundamental in statistics.

**What is an asymmetric tail?**

A symmetric distribution like the normal distribution has no skewness. An asymmetric tail is when one tail of the distribution extends further than the other.

**What is the mean value?**

The arithmetic mean is calculated by dividing the sum of all values by the number of values.

For example, an array contains these values: 3,2,1

The sum is 3 + 2 + 1 equals 6

The number of values is 3.

6/3 equals 2. The average of 3, 2, 1 is 2

**What is a probability distribution?**

A probability distribution lets you analyze how likely different random values occurs, in other words, it shows how often we would expect to see different potential values.

**How to interpret the output from the SKEW function?**

Positive skewness implies a group of values with an asymmetric tail moving toward more positive values.Ā Negative skewness implies a group of values with an asymmetric tail moving toward more negative values.

**Quartiles can also tell us about skewness**

Symmetrical distribution: Q_{2}- Q_{1} =Q_{3}- Q_{2}

Positively skewed: Q_{2}- Q_{1} < Q_{3}- Q_{2}

Negatively skewed: Q_{2}- Q_{1} > Q_{3}- Q_{2}

Learn more about quartiles: QUARTILE.INC | QUARTILE.EXC

**Box plots can also tell us about skewness**

Q1 (first quartile) - 25th percentile

Q2 (second quartile) - 50th percentile (median)

Q3 (third quartile) - 75th percentile

Positively skewed if the median is closer to Q1 than Q3. Negatively skewed if the median is closer to Q3 than Q1.

### SKEW function example

The image above shows a group of numbers in cell range B3:B17, the line chart to the right displays these values making it clear if the data is positively or negatively skewed.

Formula in cell D3:

The formula in cell D3 calculates the skewness and returns a positive value of approx. 0.194489 This means that the group of numbers are positively skewed meaning they have an asymmetric tail moving toward more positive values.

### SKEW function Syntax

SKEW(*number1, [number2], ...*)

### SKEW function Arguments

number1 |
Required. This argument can be an array ofĀ constants or a cell reference to a group of values. |

[number2] |
Optional. Up to 254 additional arguments separated by commas. |

### SKEW function not working

The SKEW function returns #DIV/0! error value if there are less than three numbers to be calculated.

### How is the SKEW function calculated?

SKEW function = n/(n-1)(n-2)Ī£(x_{i }- xĢ/s)^{3}

n - number of data points

x_{i} - data point

xĢ - arithmetic mean

s - standard deviation

**What is the standard deviation?**

Standard deviation tells you how far from the average values are spread out. Both charts above have numbers and an average plotted, they share the same average however, the numbers are not the same.

Chart A above shows that the values are more spread out than the values in chart B. Chart A has a standard deviation of 23.45256334, standard deviation for chart B is 5.207075606. Standard deviation is used in statistics.

ā(Ī£(x - xĢ)^{2}/n)

xĢĢ
is the average.

n is how many values.

### Functions in 'Statistical' category

The SKEW function function is one of many functions in the 'Statistical' category.

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