# What is the difference between mean deviation and standard deviation?

Mean deviation is the arithmetic mean of the absolute values of deviations about some point. This point can be mean, median or mode.

Standard deviation is the measure of variability or dispersion of data from its mean. It shows how much variation exists from the average.

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the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma). It is defined as the square root of the variance.

To understand standard deviation, keep in mind that variance is the average of the squared differences between data points and the mean. Variance is tabulated in units squared. Standard deviation, being the square root of that quantity, therefore measures the spread of data about the mean, measured in the same units as the data.

Said more formally, the standard deviation is the root mean square (RMS) deviation of values from their arithmetic mean.

The arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. The arithmetic mean is what students are taught very early to call the "average". If the list is a statistical population, then the mean of that population is called a population mean. If the list is a statistical sample, we call the resulting statistic a sample mean.

For example, in the population {4, 8}, the mean is 6 and the deviations from mean are {−2, 2}. Those deviations squared are {4, 4} the average of which (the variance) is 4. Therefore, the standard deviation is 2. In this case 100% of the values in the population are at one standard deviation of the mean.

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The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2,

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The mean devistion of "mean (average) of "absolute deviation" (i.e.whether  -ve of +ve difference both values are taken as +ve only) of a set of nos from a "given value". The given vaue can be "MEan, Meadian or any "reference numer" e.g find the mean deviation of a set of nos from "15". Ok?

Whereas "standard deviation is necessarily from "Mean" (besides, in standard deviation sign of -ve or +ve devation is made +ve by squaring the diference and then after getting the average (Mean) of squared sum , we have to take square root of the resuktant to compensate squaring action.

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