Describe the change to the MEAN if 1 is added to the data set below:

4, 12, 7, 0, 5, 2
*
The mean does not change
The mean increases
The mean decreases

1 answer

To find the mean, we sum up all the numbers in the data set and then divide by the total number of values.

The sum of the original data set is 4 + 12 + 7 + 0 + 5 + 2 = 30.
There are 6 numbers in the data set.

So, the mean of the original data set is 30/6 = 5.

Now, if 1 is added to the data set: 4, 12, 7, 0, 5, 2, 1,
The new sum is 30 + 1 = 31.
And the total number of values is 7 now.

So, the new mean is 31/7 ≈ 4.43.

Therefore, the mean decreases when 1 is added to the original data set.