The mean, µ, is 1, because the sum of the data is 12 and there are 12 elements.
X |
X-µ |
(X-µ)^2 |
4 |
3 |
9 |
-7 |
-8 |
64 |
0 |
-1 |
1 |
1 |
0 |
0 |
-1 |
-2 |
4 |
1 |
0 |
0 |
-4 |
-5 |
25 |
-7 |
-8 |
64 |
22 |
21 |
441 |
7 |
6 |
36 |
-5 |
-6 |
36 |
1 |
0 |
0 |
The variance is the sum of the data in the third column=680, divided by the number of elements, 12=56.67. The standard deviation, s, is the square root of this: 7.5277 approx.
Z=(X-µ)/s=(0-1)/7.53=-0.133 approx.
This means that X=0 is only 0.133 standard deviations from the mean.
The data tells us that the range is 1±7.53 minutes, that is, -6.53≤X≤8.53, so X=0 easily lies within the range.
This implies that X=0 is close to average, so it is neither significantly high or low.