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

1 Answer

The mean is increased 6 fold.

Explanation:

Recall that the mean is the sum of the values divided by the count of the values:

"mean"="sum of values"/"count of values"mean=sum of valuescount of values

For the sum of the values, let's say we have two values: x_1 and x_2x1andx2:

"mean"=(x_1+x_2)/2mean=x1+x22

And now let's multiply the values by 6 (keeping in mind that what we do to one side we must do to the other to keep the equation balanced):

6xx"mean"=(6x_1+6x_2)/26×mean=6x1+6x22

And there's our answer - the mean is increased 6 fold.