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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:

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.

Method 2: Using Built-in Functions

The second method is quicker and simpler, but it doesn’t show each calculation step. You can use Excel’s built-in functions:

To use these functions for frequency data, enter the values or cell ranges containing values and frequencies, separated by commas. For example, to calculate sample variance, use =VARA(B4:B11, C4:C11). For population variance, use =VARPA(B4:B11, C4:C11). These functions simplify the process without showing each calculation step.

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