Assumed mean method
Also called: Assumed mean, Short-cut method · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 6 "Correlation"; Class 11, Ch 8 "Use of Statistical Tools"
Meaning
The assumed mean method (short-cut method) makes it easier to work out an average. You pick a convenient value A, usually one near the middle of the data, and treat it as the mean for now. Then you work with the small deviations d = X − A instead of the large values themselves. Formula: X̄ = A + Σd/N. For a frequency distribution: X̄ = A + Σfd/Σf. The answer is exact, whatever value of A you pick. The method only saves effort. NCERT also uses it for standard deviation and correlation.
Example
Five Manipur farmers earn 500, 550, 600, 650 and 700. Take A = 550. The deviations are −50, 0, 50, 100 and 150, and Σd = 250. So X̄ = 550 + 250/5 = 600. This is the same answer as 3000/5.
Don't confuse with
- Step deviation method: goes one step further. It also divides every deviation by a common factor c, then multiplies the result back by c.