VAR.P

Calculates the variance of an entire population of data.

Syntax:

VAR.P(numberOne, [numberTwo],…)

numberOne, [numberTwo],… are 1 to 255 arguments representing the numbers that you want to use. These arguments can be numbers, cell references or ranges.

Calculation for VAR.P:

$\frac{\sum ( x - x ˉ ) ^{2}}{n}$

Example:

If numberOne, [numberTwo],… contains 1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,5,5,5,5,5:

VAR.P(1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,5,5,5,5,5)

returns 2.19047619

If numberOne, [numberTwo],… contains 1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5:

VAR.P(1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5)

returns 2.140589569

	A	B	C	D
1	1	1	1	2.140589569
2	1	2	2
3	2	2	2
4	3	3	3
5	4	4	4
6	4	5	5
7	5	5	5

Application:

Scenario: A cafe owner wants to calculate the variance of the wait times for customers during their busiest hour to understand how consistent their service is.

The owner recorded the wait times (in minutes) for every customer during the peak hour. Since they recorded data for every single customer during that specific hour, this dataset represents the entire population of wait times for that period.

Data Table: Customer Wait Times (in minutes)

	Customer ID	Wait Time (minutes)
	A	B
1	1	5
2	2	4
3	3	6
4	4	5
5	5	7
6	6	4
7	7	8
8	8	5

Calculation using VAR.P:

The VAR.P function is used to calculate the population variance of these wait times.

Function: VAR.P(5, 4, 6, 5, 7, 4, 8, 5)

Result: The result of this calculation would be 1.75.

Interpretation:

The variance of 1.75 indicates the average squared deviation of the individual wait times from the mean wait time. A low variance suggests that the wait times are clustered closely around the average, meaning the service is relatively consistent. A high variance would indicate a wider spread in wait times, suggesting inconsistency. In this case, a variance of 1.75 shows that the wait times are somewhat spread out, but not extremely so. The cafe owner can use this information to decide if they need to adjust staffing or processes to achieve more consistent service.

Result:

1.75