Assume you’re a product manager of a product with five features. You’ve been asked to find the potentiality of the features based on the customer’s happiness. How would you determine what feature has high potential, what consistently gains customer satisfaction, and what feature customers don’t like?
If you’re sitting here thinking that you don’t know how to proceed, don’t worry! This article teaches you how to calculate variance, as well as the tools and software that you need, and common mistakes to avoid.
Variance is a statistical measure representing the degree or dispersion of a set of data points (participating in the mean calculation) spread out from its mean (average). Simply put, the variance tells you how much each data point deviates from its average value.
Variance is measured in the square of the unit used. The higher the deviation from its mean, the higher the volatility which could interpret instability, unreliability, or inconsistency based on the kind of data and interpretations you are performing.
Like variance, standard deviation also measures the dispersion of data points from its mean in a given set. But, the key difference lies in the derivation. As you learned above, variance is the squared unit, but the standard deviation is calculated by square rooting the variance.
Take, for example, the age of people in two towns. The variance would give you values in squared years (which isn’t easy to directly interpret), whereas by using the SD you can directly measure the variability in years.
Variance is denoted by symbol 𝛔2:
Where:
Variance is the key component for calculating standard deviation. SD is denoted by 𝛔 and is the square root of the variance:
Now, to illustrate how to calculate variance and standard deviation, pay attention to the following example. Assume a data set of {4, 8, 6, 5, 3}:
4 − 5.2 = −1.2
8 − 5.2 = 2.8
6 − 5.2 = 0.8
5 − 5.2 = −0.2
3 − 5.2 = −2.2
(−1.2)2 = 1.44
(2.8)2 = 7.84
(0.8)2 = 0.64
(−0.2)2 = 0.04
(−2.2)2 = 4.84
Now returning to the opening scenario, imagine you collect CSAT scores (ranging from 1 to 10) for each feature over the last four quarters. One of your customer’s CSAT score sheet looks like:
Feature A — 7, 8, 7, 6
Feature B — 9, 9, 8, 9
Feature C — 5, 7, 6, 5
Feature D — 8, 8, 8, 8
Feature E — 6, 7, 7, 5
To know the potentiality of each feature for this customer, you need to know the volatility in the customer’s satisfaction score. To find this using the above data first, you need to calculate the mean CSAT of each feature:
Feature A — (7+8+7+6) / 4 = 7.0
Feature B — (9+9+8+9) / 4 = 8.75
Feature C — (5+7+6+5) / 4 = 5.75
Feature D — (8+8+8+8) / 4 = 8.0
Feature E — (6+7+7+5) / 4 = 6.25
Using the mean (average) from above, you would then calculate the volatility (variance) of each feature by doing:
Feature A — ((7−7)2 + (8−7)2 + (7-7)2 + (6-7)2) / 4 = 2 / 4 = 0.5
Feature B — ((9−8.75)2 + (9−8.75)2 + (8-8.75)2 + (9-8.75)2) / 4 = 0.75 / 4 = 0.1875
Feature C — ((5−5.75)2 + (7−5.75)2 + (6-5.75)2 + (5-5.75)2) / 4 = 2.75 / 4 = 0.6875
Feature D — ((8−8)2 + (8−8)2 + (8-8)2 + (8-8)2) / 4 = 0 / 4 = 0
Feature E — ((6−6.25)2 + (7−6.25)2 + (7-6.25)2 + (5-6.25)2) / 4 = 2.75 / 4 = 0.6875
However, if you look at feature A, it says that there is a 0.5 variance in customer satisfaction scores with respect to its mean of 7.0. This indicates that the customer happiness rating given by this customer will be closer to the mean.
To find the potentiality, you need an additional step to calculate the standard deviation present in these numbers from the mean. You do this with:
Feature A — Sqrt(0.5) = 0.71
Feature B — Sqrt(0.1875) = 0.43
Feature C — Sqrt(0.6875) = 0.83
Feature D — Sqrt(0) = 0
Feature E — Sqrt(0.6875) = 0.83
How do you interpret this? If you see Feature A, the standard deviation is 0.71, which means, most of the CSAT scores given by users for Feature A would vary between -0.71 to +0.71 from the mean (average). Since the value is low, it shows the customer (users) have a consistent experience from this feature.
Now, looking at the standard deviation of each feature for this one customer, we can conclude that:
While variance can be a great tool, it also comes with its fair share of cons. Review the following list to make a more informed decision about its potential adoption:
Pros
Cons
When calculating variance, make sure to avoid:
Calculating variance manually can be a difficult and time consuming task. To help with this, try automating your process with some of the following tools:
Variance is a fundamental statistical measure that quantifies the spread or dispersion of data points within a dataset. Understanding variance is crucial for analyzing data, assessing risk, and making informed decisions in product management.
By accurately calculating and interpreting variance, you can gain deeper insights into data patterns, identify areas for improvement, and make more informed decisions. Good luck with your calculations and be sure to comment with any questions!
Featured image source: IconScout
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