Standard deviation
Also called: SD · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 1 "Introduction (Statistics for Economics)"; Class 11, Ch 2 "Collection of Data"; Class 11, Ch 6 "Correlation"; Class 11, Ch 8 "Use of Statistical Tools"
Meaning
Standard deviation (SD) measures how widely values are spread around their arithmetic mean. It is the positive square root of the variance: σ = √[Σ(X − X̄)²/N]. It is in the same units as the data, such as rupees or kg, so it is easy to read. It is the most widely used absolute measure of dispersion (spread). An average means little without it: a river's "average depth" can hide a spot deep enough to drown someone.
Example
In a survey of 100 households, the mean monthly family income was Rs 18,000 and the SD was Rs 9,000. Incomes were therefore widely spread around the average. For toothpaste spending, the mean was Rs 104 a month and the SD was Rs 35.60.
Don't confuse with
- Variance: variance is the square of the SD, so it is in squared units (for example, rupees²). The SD brings the measure back to 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