#### How to Calculate the Variance of a Frequency Distribution in Excel

Frequency data, in simple terms, records how often specific values or categories appear in a dataset. For instance, it could show how many students scored within certain test score ranges or how many cars were sold by different brands in a month. It’s important for understanding the distribution of values in your dataset.

To calculate the variance of frequency data, you’ll use a formula that’s a bit different from the standard one. The formula for variance of a frequency distribution looks like this:

Variance = ∑ f(x – 𝑥̄)² / ∑ f

Here’s what each part of the formula represents:

• f: The frequency of each value or category.
• x: The value or category.
• 𝑥̄: The mean of the frequency distribution.
• ∑: Indicates summation, meaning adding up all the values.

## Method 1: Using Mathematical Formulas

Excel can automate these calculations, making the process more efficient. Here are the steps:

1. Calculate the Mean: Use the formula =SUMPRODUCT(B2:B10, C2:C10) / SUM(C2:C10), where B2:B10 has the values or categories, and C2:C10 has their frequencies.
2. Squared Differences: Calculate the squared difference between each value or category and the mean using the formula =C2*(B2-\$D\$2)^2. Fill this formula down to calculate squared differences for all data points.
3. Sum of Squared Differences: Find the sum of the squared differences with the formula =SUM(D2:D10).
4. Calculate Variance: For sample data, use =SUMPRODUCT((midpoints – mean)^2, frequencies) / (SUM(frequencies) – 1). For population data, use =SUMPRODUCT((midpoints – mean)^2, frequencies) / SUM(frequencies).

This method offers transparency and control over the calculations.