Question

Complete the data set with one value so that the mean of the data is 13. 10,14,8,16,12, ? Which value can you remove from the new set of data so that the mean is 14

Answer 1

The mean is the sum of the elements in the dataset, divided by the cardinality of the dataset.

So, the mean of the dataset (including the unknown element) is

$\dfrac{10+14+8+16+12+x}{6}=\dfrac{60+x}{6}$

We want the mean to be 13, so we want

$\dfrac{60+x}{6}=13$

Multiply both sides by 6:

$60+x=78$

Subtract 60 from both sides:

$x=18$

So, the new dataset is

$10,14,8,16,12,18$

If we remove one element, we will be left with a dataset of 5 elements. If we want the mean to be 14, the sum of the elements must be 14*5 = 70.

The sum of the 6 elements is 78, so we have to remove the 8. The new dataset will be

$10,14,16,12,18$

and in fact the mean is

$\dfrac{10+14+16+12+18}{5}=\dfrac{70}{5}=14$