Step deviation 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 step deviation method is a short-cut that builds on the assumed mean method. First take deviations from an assumed mean A. Then divide each deviation by a common factor c, often the class width, so the numbers become small. Here d′ = (X − A)/c. The mean is X̄ = A + (Σd′/N) × c, or A + (Σfd′/Σf) × c for grouped data. The same idea is used for standard deviation and correlation. Karl Pearson's r does not change when the origin and scale are changed this way, so r can be calculated from the small numbers directly.
Example
Farm incomes 500, 550, 600, 650 and 700, with A = 550 and c = 50. Then d′ = −1, 0, 1, 2, 3, and Σd′ = 5. So X̄ = 550 + (5/5) × 50 = 600.
Don't confuse with
- Assumed mean method: uses the deviations X − A without dividing them by c. Step deviation adds that division and then multiplies the result back by c.