STDEV

Returns the sample standard deviation of the arguments.

Syntax:

STDEV(number1, number2, ... number30)

number1 to number30 are up to 30 numbers or ranges containing numbers.

STDEV returns the standard deviation where number1 to number30 are a sample of the entire population. With N values in the sample, the calculation formula is:

$\frac{1}{N - 1} \sum_{i - 1}^{N} (x_{i} - \overline{x})^{2}$

Example:

STDEV(2, 6, 4)

returns 2.

Application:

Imagine you are the manager of a call center and you want to measure the variability in the average call handling time for your team. You randomly sample the call handling times (in seconds) of 10 agents on a given day.

Here is the data in a table:

	Agent	Call Handling Time (seconds)
	A	B
1	1	240
2	2	255
3	3	262
4	4	248
5	5	270
6	6	258
7	7	265
8	8	250
9	9	245
10	10	267

To calculate the sample standard deviation using the STDEV function, you would apply the function to this range of values.

The formula for the sample standard deviation is:

$s = \frac{\sum _{i = 1}^{n} ( x _{i} - x ˉ ) ^{2}}{n - 1}$

Where:

s is the sample standard deviation
$x_{i}$ is each individual value
$\overset{x}{ˉ}$ is the sample mean
n is the number of samples

Step 1: Calculate the mean ( $\overset{x}{ˉ}$ )

Sum of all values = 240+255+262+248+270+258+265+250+245+267=2560

Number of samples (n) = 10

Mean ( $\overset{x}{ˉ}$ ) = 2560/10=256

Step 2: Calculate the squared difference from the mean for each value

	Agent	Call Handling Time (seconds)	Difference from Mean ( $x_{i} - \overset{x}{ˉ}$ )	Squared Difference ( $x_{i} - \overset{x}{ˉ}$ )2
	A	B	C	D
1	1	240	-16	256
2	2	255	-1	1
3	3	262	6	36
4	4	248	-8	64
5	5	270	14	196
6	6	258	2	4
7	7	265	9	81
8	8	250	-6	36
9	9	245	-11	121
10	10	267	11	121
11	Sum			916

Step 3: Apply the STDEV formula

The STDEV function would automatically perform these calculations. The formula would be applied as:

STDEV(240,255,262,248,270,258,265,250,245,267)

$s = \frac{916}{10 - 1}$

$s = \frac{916}{9}$

$s = 101.78$

$s \approx 10.09$

The correct sample standard deviation is approximately 10.09 seconds. This means the typical variation in call handling time is about 10.09 seconds away from the average of 256 seconds. A lower standard deviation would indicate that your team's call handling times are more consistent, while a higher one would suggest greater variability. This is valuable information for performance management and training purposes.

Result for STDEV:

10.09

	Agent	Call Handling Time (seconds)	Difference from Mean ( $x_{i} - \overset{x}{ˉ}$ )	Squared Difference ( $x_{i} - \overset{x}{ˉ}$ )2
	A	B	C	D
1	1	240	-16	256
2	2	255	-1	1
3	3	262	6	36
4	4	248	-8	64
5	5	270	14	196
6	6	258	2	4
7	7	265	9	81
8	8	250	-6	36
9	9	245	-11	121
10	10	267	11	121
11	Sum			916

	Agent	Call Handling Time (seconds)	Difference from Mean ( $x_{i} - \overset{x}{ˉ}$ )	Squared Difference ( $x_{i} - \overset{x}{ˉ}$ )2
	A	B	C	D
1	1	240	-16	256
2	2	255	-1	1
3	3	262	6	36
4	4	248	-8	64
5	5	270	14	196
6	6	258	2	4
7	7	265	9	81
8	8	250	-6	36
9	9	245	-11	121
10	10	267	11	121
11	Sum			916

	Agent	Call Handling Time (seconds)	Difference from Mean ( $x_{i} - \overset{x}{ˉ}$ )	Squared Difference ( $x_{i} - \overset{x}{ˉ}$ )2
	A	B	C	D
1	1	240	-16	256
2	2	255	-1	1
3	3	262	6	36
4	4	248	-8	64
5	5	270	14	196
6	6	258	2	4
7	7	265	9	81
8	8	250	-6	36
9	9	245	-11	121
10	10	267	11	121
11	Sum			916