Can the standard deviation ever be negative?

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Answer


Edison

Standard Deviation formula is computed using squares of the numbers. Square of a number cannot be negative. Hence Standard deviation cannot be negative.

Initially, we should stop for a minute and consider what standard deviation speaks to.

It gauges fluctuation in an informational index.

When you have some arrangement of numbers and compute its standard deviation, the subsequent number guides you to what degree the individual numbers in the set are not the same as one another. In the event that all are about the equivalent (like 252, 249, 253, 251, 254), standard deviation will be moderately little. On the off chance that there are enormous contrasts (like 252, 11, 840, 305, 64, 5846), standard deviation will be a lot greater.

Consider the possibility that every one of the numbers in the informational index are the very same (like 252, 252, 252, 252, 252, 252. At that point standard deviation will be actually zero.

Would you be able to get a much littler standard deviation (which would need to be negative)? No. You can't have an informational collection which is less various than one where all numbers are the equivalent, correct?

To finish up, the littlest conceivable esteem standard deviation can reach is zero. When you have at any rate two numbers in the informational index which are not actually rise to each other, standard deviation must be more noteworthy than zero – positive. By no means can standard deviation be negative.

Example1:

Are standard deviations always positive?

No, standard deviation is constantly positive or 0. When you square deviations from the mean, they become positive or zero. Their total is as yet positive or zero and the remainder in the wake of partitioning the total by n – 1 remains positive or zero. This last amount is the fluctuation.

Example2:

Can standard deviation be bigger than mean?

The standard deviation is a portrayal of the information's spread, how broadly it is conveyed about the mean. A littler standard deviation demonstrates that a greater amount of the information is bunched about the mean. A bigger one shows the information are progressively spread out. ... In the principal case, the standard deviation is more prominent than the mean.

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