How to calculate variance
As established earlier, it’s important to know how variance is calculated. Here is a simplified version of the variance formula:
s^2= [Y [X - x^2] divided by (n - 1)
s^2 = sample variance
Y = sum of…
Χ = each value
x = sample mean
n = number of values in the sample
When you measure variance, you're calculating the mean or average of your data points. By squaring the differences and dividing the squares by the total number of data points, you can get a good idea of how well (or not) you are meeting measured goals.
Here’s how you calculate business variances:
- Determine the mean of your data.
- Find the difference of each value from the mean.
- Square each difference.
- Calculate the squared values.
- Divide this sum of squares by n – 1 (sample) or N (population).
For the easiest route, find an online variance calculator or Excel workbook set up to do the heavy calculating for you.
Example of calculating variance
Usually, companies use software to calculate business variances. However, it can be useful to do so manually until you fully understand the process. This example will use six numbers representing the sale of a particular product.
Sales over a six-month period: 41, 46, 69, 60, 52, 32 (This is your data set.)
Step 1: What’s the mean (average)?
Add the sales number and divide by six (number of data points).
Mean = (41 + 46 + 69 + 60 + 52 + 32) ÷ 6 = 50
Step 2: What’s the deviation for each sales number?
Remember, 50 is the mean. So, subtract 50 from each sales number.
41 – 50 = -9
46 – 50 = -4
69 – 50 = 19
60 – 50 = 10
52 – 50 = 2
32 – 50 = -18
Step 3: Square each deviation
Multiply each deviation from the mean to get all positive numbers:
(-9)2 = -9 × -9 = 81
(-4)2 = -4 × -4 = 16
192 = 19 × 19 = 361
102 = 10 × 10 = 100
22 = 2 × 2 = 4
(-18) 2 = -18 × -18 = 324
Step 4: What is the sum of squares?
Add up the squared deviations to get the sum of the squares.
81 + 16 + 361 + 100 + 4 + 324 = 886
Step 5: Divide by n – 1 or N
In this case (a sample), we’ll divide this result by n – 1, where n is the number of data points (6).
886 ÷ (6-1) = 886 ÷ 5 = 177.2
The next step is brainstorming ways to achieve more consistently positive results to move your sales efforts forward.
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