What is the STDEV.S function?

The STDEV.S function returns standard deviation based on a sample.

What is 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 exact 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 fundamental in statistics.

What is the difference between the STDEV.P function and the STDEV.S function?

STDEV.P function calculates the standard deviation for a population and the STDEV.S function calculates the standard deviation for a sample. STDEV.P uses the count of all values (n) in the denominator.
STDEV.S uses (n-1) in the denominator (Bessel's correction). This accounts for the difference between sample variance and population variance in statistics. STDEV.S is better for sample inferential statistics.

STDEV.P math formula:

STDEV.S math formula:

When to use the STDEV.P function and the STDEV.S function?

Use STDEV.P if you have the full population data. Use STDEV.S if you have a sample of limited data from a larger population. STDEV.P will result in a lower standard deviation compared to STDEV.S on the same data.

Sample standard deviation is considered a better estimate for inferring population parameters.

What is inferring population parameters?

Population parameters refer to the actual values of statistics that describe an entire population, such as the population mean or standard deviation. However, the true population parameter values are often not known.

What is sample inferential statistics?

Sample inferential statistics are methods that allow using statistics calculated on a sample of data to infer the unknown population parameters.

For example:

• The sample mean can be used to estimate the population mean.
• The sample standard deviation can estimate the population standard deviation.

1. STDEV.S Function Syntax

STDEV.S(number1, [number2], ...)

2. STDEV.S Function Arguments

number1	Required. The first number argument that represents a sample of the population.
[number2]	Optional. Up to 253 additional number arguments.

The STDEV.S function ignores logical values and text values.

For large sample sizes, STDEV.S and STDEV.P return approximately equal outputs.

3. STDEV.S Function Example

Formula in cell D3:

Explaining the formula

Here is the math formula Excel uses for calculating the standard deviation for a sample size:

x is each value
x ̅ is the average of all values
n is the number of values

Step 1 - Calculate the average

137+139+141+105+139+124+126+146+105+101 equals 1263.

1263/10 equals 126.3

Step 2 - Subtract the average from each value

137-126.3 = 10.7
139-126.3 = 12.7
141-126.3 = 14.7
105-126.3 = 21.3
139-126.3 = 12.7
124-126.3 = -2.3
126-126.3 = -0.3
146-126.3 = 19.7
105-126.3 = -21.3
101-126.3 = 25.3

Step 3 - Calculate the square

10.7^2 = 114.49
12.7^2 = 161.29
14.7^2 = 216.09
-21.3^2 = 453.69
12.7^2 = 161.29
-2.3^2 = 5.29
-0.3^2 = 0.09
19.7^2 = 388.09
-21.3^2 = 453.69
-25.3^2 = 640.09

Step 4 - Sum numbers

114.49+161.29+216.09+453.69+161.29+5.29+0.09+388.09+453.69+640.09 equals 2594.1

Step 5 - Divide sum by count minus 1

2594.1/(10-1)

becomes

2594.1/9

equals

288.233333333333

Step 6 - Calculate the square root

288.233333333333^(1/2) equals 16.9774360058677

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4. Sort rows by sample standard deviation

The image above shows a formula in cell B8 that sorts rows from cell range B3:N6 by the standard deviation of a sample from large to small. Column P contains these measures.

Explaining formula

Step 1 - Calculate the standard deviation of a sample

STDEV.S(a)

Step 2 - Build the LAMBDA function

The LAMBDA function build custom functions without VBA, macros or javascript.

Function syntax: LAMBDA([parameter1, parameter2, …,] calculation)

LAMBDA(a,STDEV.S(a))

Step 3 - Calculate the standard deviation of a sample by row

The BYROW function puts values from an array into a LAMBDA function row-wise.

Function syntax: BYROW(array, lambda(array, calculation))

BYROW(C3:N6,LAMBDA(a,STDEV.S(a)))

returns

{226.967091460548; 297.500445632465; 308.956699918035; 212.224937842904}

Step 4 - Sort rows based on the standard deviation of a sample

The SORTBY function sorts a cell range or array based on values in a corresponding range or array.

Function syntax: SORTBY(array, by_array1, [sort_order1], [by_array2, sort_order2],…)

SORTBY(B3:N6,BYROW(C3:N6,LAMBDA(a,STDEV.S(a))),-1)

becomes

SORTBY(B3:N6,{226.967091460548; 297.500445632465; 308.956699918035; 212.224937842904},-1)

and returns

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Functions in 'Statistical' category

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

Excel function categories

Excel categories

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