Variance
Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 1 "Introduction (Statistics for Economics)"; Class 11, Ch 6 "Correlation"
Meaning
Variance measures how spread out the values in a set of data are. It is the mean of the squared deviations from the arithmetic mean: σ² = Σ(X − X̄)²/N. The deviations are squared so that the minus and plus signs do not cancel out. Without squaring, deviations from the mean always add up to zero. A larger variance means the values are more scattered, and zero means all values are equal.
Example
Five farmers in Manipur earn 500, 550, 600, 650 and 700, so the mean is 600. The squared deviations are 10,000, 2,500, 0, 2,500 and 10,000. They total 25,000, so the variance is 25,000 ÷ 5 = 5,000.
Don't confuse with
- Standard deviation: the SD is the square root of the variance (here √5,000 ≈ 70.7). Unlike the variance, it is in the data's own units.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class