The direct method gives huge multiplications and I run out of time. My friend mentioned an assumed mean shortcut. How does it work?
In the assumed mean method, you pick a convenient class mark 'a' (usually one near the middle) and work with deviations instead of large numbers. For each class, compute the class mark xᵢ, then the deviation dᵢ = xᵢ − a. Multiply each fᵢ by its dᵢ, sum these up, and use Mean = a + (Σfᵢdᵢ / Σfᵢ). The deviations are small numbers, often multiples of the class width, so the arithmetic is much lighter. For example, if a = 25, Σfᵢdᵢ = 120 and Σfᵢ = 60, then Mean = 25 + 120/60 = 25 + 2 = 27. The answer is identical to the direct method but with far less calculation, which saves valuable exam time.
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