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?

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Answer 1 · 2018-03-02T14:15:14

The mean is increased 6 fold.

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

$mean = \frac{sum of values}{count of values}$ $"mean"="sum of values"/"count of values"$

For the sum of the values, let's say we have two values: $x_{1} and x_{2}$ $x_1 and x_2$ :

$mean = \frac{x_{1} + x_{2}}{2}$ $"mean"=(x_1+x_2)/2$

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):

$6 \times mean = \frac{6 x_{1} + 6 x_{2}}{2}$ $6xx"mean"=(6x_1+6x_2)/2$

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