How to use the STDEV.P function

What is the STDEV.P function?

The STDEV.P function returns standard deviation based on the entire population. STDEV.P is an abbreviation of standard deviation population. The STDEV.P function and the STDEV.S functions replaces the outdated STDEV function.

1. Introduction

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.

A normal distribution is a symmetric, bell-shaped probability distribution that is commonly used in statistics and probability theory. The shape of the normal distribution is determined by its mean (μ) and standard deviation (σ). The mean represents the center of the distribution, while the standard deviation represents the spread or dispersion of the data around the mean.

• A normal distribution with a standard deviation of 0.5 is relatively narrow and tightly clustered around the mean.
  
  The values in the distribution are concentrated within a smaller range, with most values falling closer to the mean. The curve appears tall and steep, indicating a higher concentration of data points near the mean.
• A normal distribution with a standard deviation of 1 is the most commonly used normal distribution, often referred to as the standard normal distribution.
  
  The standard deviation of 1 represents a moderate spread of the data around the mean. About 68% of the data falls within one standard deviation (±1σ) of the mean, and approximately 95% of the data falls within two standard deviations (±2σ) of the mean. The curve has a characteristic bell shape, with a smooth and gradual taper towards the tails.
• A normal distribution with a standard deviation of 2 is relatively wide and spread out compared to the standard normal distribution. The data is dispersed over a larger range, with values more spread out from the mean. The curve appears shorter and flatter, indicating a lower concentration of data points near the mean.

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.

2. STDEV.P function Syntax

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

3. STDEV.P function Arguments

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

4. STDEV.P function Example 1

You have a dataset containing the commute time of employees in a company. Calculate the population standard deviation of the time values to understand the spread of commute time across the organization?

Here are the data points:

Commute time
40
76
60
31
27
42
60
59
42
43

The argument is:

number1 = B16:B25

The data points are specified in cells B16:B25 in the image above.

Lets assume the data follows a normal distribution. The image above shows a chart containing a blue curve representing the probability mass function of a normal distribution where the mean is 48 and the standard deviation is calculated below. The black lines represents the standard deviations denoted σ.

The formula returns 14.44 which represents the standard deviation value. The image above shows the different standard deviations in the chart.

Formula in cell D3:

1σ = 14.44
2σ = 28.87
3σ = 43.31

-1σ = -14.44
-2σ = -28.87
-3σ = -43.31

These values are added or subtracted to the average based on the sign. The average is 48.

1σ = 48 + 14.44 =  62.44
2σ = 48 + 28.87 = 76.87

-1σ = 48 - 14.44 = 33.56
-2σ = 48 - 28.87 = 19.13

In the image above, locate the value 62.44 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the blue curve, which represents the probability mass function for a normal distribution. Then, follow the point of intersection horizontally towards the y-axis to the left. You will find that the corresponding value on the y-axis is approximately 0.164.

You can calculate the y value using the NORM.DIST function:

It returns approximately 0.164.

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

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

5. STDEV.P function Example 2

In a manufacturing process, you measure the length of a product across multiple batches. Use the STDEV.P function to calculate the population standard deviation of the product lengths to assess the variability in the manufacturing process?

Here is the data:

Length
81
88
102
109
114
109
103
106
89
100

The argument is:

number1 = B16:B25

The data points are specified in cells B16:B25 in the image above.

Lets assume the data follows a normal distribution. The image above shows a chart containing a blue curve representing the probability mass function of a normal distribution where the mean is 100.1 and the standard deviation is calculated below. The black lines represents the standard deviations denoted σ.

The formula returns 10.16 which represents the standard deviation value. The image above shows the different standard deviations in the chart.

Formula in cell D3:

1σ = 10.16
2σ = 20.32
3σ = 30.64

-1σ = -10.16
-2σ = -20.32
-3σ = -30.64

These values are added or subtracted to the average based on the sign. The average product length is 100.1.

1σ = 100.1 + 10.16 =  110.26
2σ = 100.1+ 20.32 = 120.42

-1σ = 100.1- 10.16 = 89.94
-2σ = 100.1- 20.32 = 79.77

In the image above, locate the value 110.26 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the blue curve, which represents the probability mass function for a normal distribution. Then, follow the point of intersection horizontally towards the y-axis to the left. You will find that the corresponding value on the y-axis is approximately 0.024.

You can calculate the y value using the NORM.DIST function:

The NORM.DIST function returns approximately 0.024.

6. How is the output from the STDEV.P function calculated?

The STDEV.P function is entered in cell D3, here is how the function calculates the output:

x ̅ is the average.
n is how many values.

Step 1 - Calculate the average

137+139+141+105+139+124+126+146+105+101 = 1263

1263/10 = 126.3

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

(137-126.3)^2+(139-126.3)^2+(141-126.3)^2+(105-126.3)^2+(139-126.3)^2+(124-126.3)^2+(126-126.3)^2+(146-126.3)^2+(105-126.3)^2+(101-126.3)

becomes

(10.7)^2+(12.7)^2+(14.7)^2+(-21.3)^2+(12.7)^2+(-2.3)^2+(-0.299999999999997)^2+(19.7)^2+(-21.3)^2+(-25.3)

becomes

114.49+161.29+216.09+453.69+161.29+5.29+0.0899999999999982+388.09+453.69+640.09

and returns

2594.1

Step 3 - Divide with the total count

2594.1/10 equals 259.41

Step 4 - Square root the result

259.41^(1/2) equals 16.1062099824881

Recommended articles

• Standard Deviation Calculator
• Standard Deviation Formulas

Functions in 'Statistical' category

The STDEV.P function is one of 73 functions in the 'Statistical' category.

Excel function categories

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