are standard deviations additive
In a population P with roughly normal distribution, mean M, and standard deviation σ: 1  2/3s of the values in P will be. 2  95% of the values will be within the range M +/- 2σ. 3  99% of the values will be within the range M +/- 3σ. If we simply. computed the average deviation of each value from the mean (the step 2. values)–we would always get a result of zero! (This is because the positive. deviations would cancel the negative deviations.) Squaring and “un-squaring”. resolves this issue and ensures that our standard deviation will have the same. In a population P with roughly normal distribution, mean M, and standard deviation σ: 1  2/3s of the values in P will be. within the range M +/- σ. 2  95% of the values will be within the range M +/- 2σ. 3  99% of the values will be within the range M +/- 3σ. Best Answer: It is saying: if you take two sets or distributions and add them together, then is the standard deviation of the new set equal to the sum of the standard deviations of the two separate sets? The answer is no, because standard deviation is the square root of the differences of the values from the mean. And square roots are not additive. For point 1) there is no particular reason to use the standard deviation as a measure of spread, except for when you have a normal sampling distribution. The measure $E(|X-\mu|)$ is a more appropriate measure in the case of a Laplace Sampling distribution. If the goal of the standard deviation is to summarise the spread of a symmetrical data set (i.e. in general how far each datum is from the mean), then we need a good method of defining how to measure that spread. The benefits of squaring include: Squaring always gives a positive value, so the sum will not be zero. One way you can think of this is that standard deviation is similar to a distance from the mean. Compare this to distances in euclidean space - this gives you the true distance, where what you suggested (which, btw, is the absolute deviation) is more like a manhattan distance calculation. The standard deviation describes the spread of the data, and is the basis for how we compute things like the degree of certainty, the margin of error, etc. Suppose we have a population of data points, P={p1,…,pn}. We know that the mean is. the sum of the points (pis) divided by the number of. As shown below, the larger the standard deviation, the more. dispersion there is in the process data. All three processes above have a mean (average) of 10, but the standard. deviations vary. A smaller standard deviation means greater consistency, predictability and quality. Rule 4. The expected value or mean of the sum of two random variables is the sum of the means. This is also known as the additive law of expectation. E(X+Y) = E(X)+E(Y) Formulas and Rules for the Variance, Covariance and Standard Deviation of Random Variables. Formulas for the Variance.
No, standard deviations are not additive.