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.
