# If you were to multiply each value in a data set by 6, what effect would this have on the standard deviation of the data set?

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Feb 14, 2015

The standard deviation would also be multiplied by 6.

Because the mean would also be 6x larger, the differences from the mean would be 6x larger too.

It is the same idea as if you were looking at your data set through an enlarging lens-- everything would be 6x bigger, not only the data values, but also the mean, the differences from the mean, but just everything!

Extra :
The variance would be 36x larger, because variance is based on the squares of differences. But since standard deviation is the square root of the variance, this cancels out.

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