# How to use the STDEV function

**What is the STDEV function?**

The STDEV function calculates the standard deviation of a sample of values. The standard deviation shows how much the values differ from the mean value.

There are two different math formulas for calculating the standard deviation, the STDEV function tries estimates the standard deviation based on a sample of values whereas the STDEV.P function calculates the standard deviation based on the entire population.

Section 5 below describes the differences in how the standard deviation is calculated.

There are newer better functions that may have improved accuracy, this function is available for compatibility with older workbooks created in earlier Excel versions and other older software.

The new STDEV.S function replaces the older STDEV function which has better accuracy, Microsoft tells us that the STDEV function may not be available in future Excel versions and recommends us using the STDEV.S from now on.

### Table of Contents

## 1. What is Standard Deviation?

Standard deviation tells you how far from the mean 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. Standard deviation is used in statistics.

A low standard deviation number near 0 (zero) tells us that the data points are located very close to the mean, a larger standard deviation value indicates data points are more spread out from the mean.

The most commonly used symbol for standard deviation is Ïƒ which is the lower case greek letter sigma. Ïƒ was chosen because standard deviation is calculated using summation Î£ which is the upper case greek letter sigma.

Ïƒ is used to represent population standard deviation. s is used to represent sample standard deviation. In statistics formulas, Ïƒ is used along with the mean symbol Î¼ to represent a distribution.

**What is the mean?**

The mean is also called the average. The mean is calculated by adding all the values in a dataset and dividing by the total number of values. Excel has functions for calculating the average. AVERAGE function

For example, a data set contains 5, 2,6,8, and 4. The total is 5 + 2 + 6 + 8 + 4 equals 25. The average is 25 / 5 equals 5.

**What is one standard deviation in a normal distribution?**

One standard deviation from the mean Î¼ captures 34.13% of the data on each side, or 68.27% total in a standard normal distribution. This percentage allows standard deviations to indicate where values fall in the distribution.

**What is two standard deviations in a normal distribution?**

Two standard deviations from the mean Î¼ captures 47.5% of the data on each side, or 95% total in a standard normal distribution.

**What is three standard deviations in a normal distribution?**

Tree standard deviations from the mean Î¼ captures 48.85% of the data on each side, or 97.7% total in a standard normal distribution.

## 2. STDEV Function Syntax

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

## 3. STDEV Function Arguments

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

[number2] |
Optional. Up to 254 additional arguments. |

## 4. STDEV Function Example

Formula in cell C3:

## 5. How is the STDEV function calculated?

The STDEV function is entered in cell D3, here is how the function calculated the output:

x Ì… is the average.

n is how many values.

#### Step 1 - Calculate the average

14 + 18 + 30 + 26 + 67 + 35 + 41 + 2 + 80 + 16 + 48 + 58 = 435

435/12 = 36.25

#### Step 2 - Subtract the average and square the result for all values

(14-36.25)^2 + (18-36.25)^2 + (30-36.25)^2 + (26-36.25)^2 + (67-36.25)^2 + (35-36.25)^2 + (41-36.25)^2 + (2-36.25)^2 + (80-36.25)^2 + (16-36.25)^2 + (48-36.25)^2 + (58-36.25)^2

becomes

(-22.25)^2+(-18.25)^2+(-6.25)^2+(-10.25)^2+(30.75)^2+(-1.25)^2+(4.75)^2+(-34.25)^2+(43.75)^2+(-20.25)^2+(11.75)^2+(21.75)^2

becomes

495.0625+333.0625+39.0625+105.0625+945.5625+1.5625+22.5625+1173.0625+1914.0625+410.0625+138.0625+473.0625

and returns

6050.25

#### Step 3 - Divide with the total count minus 1

6050.25/11 equals 550.022727272727

#### Step 4 - Square root the result

550.022727272727^(1/2) equals 23.4525633411942

## 6. What is the difference between the STDEV function and the STEDV.P function?

The STDEV function estimates an output based on a sample of values, the STEDV.P however, calculates the standard deviation based on the entire population of values.

STDEV function formula:

STDEV.P function formula:

These formula differences explain why the functions return different values even if you use the same values.

## 7. What is the difference between the standard deviation and variance?

Standard deviation measures the amount of dispersion around the mean, while variance represents the average squared deviation. Standard deviation provides an interpretable and tangible idea of spread, while variance is a more abstract representation. In general, standard deviation is more widely used and reported than variance, as it's more understandable.

VAR function formula:

STDEV function formula:

The math formulas above demonstrates that standard deviation is the square root of the variance.

### Functions in 'Compatibility' category

The STDEV function function is one of 21 functions in the 'Compatibility' category.

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