Mean deviation
Also called: Average deviation, Mean absolute deviation · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 2 "Collection of Data"
Meaning
Mean deviation is a measure of dispersion, which means a number showing how widely values are spread. It is the average distance of the values from a central value (the mean or the median). Negative and positive signs are ignored, so every distance counts as positive (the absolute deviation). It is easy to understand and uses every value. But because the signs are dropped, it is hard to use in further algebra. For that reason, standard deviation is used more often in advanced work.
Mean deviation = Σ|X − A|/N, where A is the mean or the median
Example
Take the values 2, 4 and 6. The mean is 4. The distances from 4 are 2, 0 and 2. Mean deviation = (2 + 0 + 2)/3 ≈ 1.33.
Don't confuse with
- Standard deviation: it squares the deviations instead of dropping their signs, then takes the square root of the average. This makes it easier to use in algebra.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class