Question

Create a data set of 15 numbers where the mean and median are both 59 and the standard deviation is between 10 and 11. Then, add an outlier to your data set. How are the mean and standard deviation affected

Answer 1

What we should do is create a set of 15 data.

To comply with the mean and median 59, what we will do is make our center point 59, we will add 7 values ​​backwards and 7 values ​​forward, always the same value adding in the case forward or subtracting in the case of backwards the same number so that the mean is not affected

So:

We will add 2.5 in the same proportion, we start with the forward ones:

59 + 2.5 * 1 = 61.5

59 + 2.5 * 2 = 64

59 + 2.5 * 3 = 66.5

59 + 2.5 * 4 = 69

59 + 2.5 * 5 = 71.5

59 + 2.5 * 6 = 74

59 + 2.5 * 7 = 76.5

Backward:

59 - 2.5 * 7 = 41.5

59 - 2.5 * 6 = 44

59 - 2.5 * 5 = 46.5

59 - 2.5 * 4 = 49

59 - 2.5 * 3 = 51.5

59 - 2.5 * 2 = 254

59 - 2.5 * 1 = 56.5

Therefore, the entire data set would be:

41.5, 44, 46.5, 49, 51.5, 54, 56.5, 59, 61.5, 64, 66.5, 69, 71.5, 74, 76.5

We guarantee the mean and median 59.

The standard deviation is equal to 10.8

Now if we change the first value of 41.5 by 1000, we will see what happens:

New dataset:

1000, 44, 46.5, 49, 51.5, 54, 56.5, 59, 61.5, 64, 66.5, 69, 71.5, 74, 76.5

The mean changes to 122.9

And the standard deviation to 234.62

In other words, there is a significant increase in the mean, but in the standard deviation the growth is abysmal.

I attach an excel to check all this data.