Pooling Two Group Averages

Pooling Two Group Averages — medium Descriptive Statistics problem | Incognition

Weighted Mean Lab

Explore how values and their corresponding weights combine to pull the average.

Frequency Weights

Observation Value (x)	Frequency / Weight (w)	Weighted Contribution (x × w)
Totals:	Sum of Freqs = 0	Sum of Products = 0

Method 1: Expanded Arithmetic Mean

Write out every value and take their ordinary average:

Values: [2, 2, 2, 5, 5, 8]
Mean = (2+2+2+5+5+8) / 6 = 24/6 = 4.0

Method 2: Weighted Mean using Frequencies

Multiply each unique value by its frequency and divide by total count:

Mean = (2×3 + 5×2 + 8×1) / (3+2+1)
= (6 + 10 + 8) / 6 = 24/6 = 4.0

Frequency is a Weight: By using frequency as a weight, we do not have to write out thousands of raw, repeated observations. The weighted mean gives us the exact same result as averaging the full, expanded dataset, which makes it extremely useful in grouping big data!

Pooling Two Group Averages

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Weighted Mean Lab