Example:
measured values xi |
round | |
| x1 | 74 | |
| x2 | 77 | |
| x3 | 91 | |
| x4 | 73 | |
| x5 | 81 | |
| arithmetic mean x | 79 | 79 |
| R = xmax - xmin = | 18 | |
| kn = | 0.430 | |
| s = R . kn = | 7.74 | 7.7 |
| sr= (s / x) . 100 [%] = | 9.772727 | 9.8 [%] |
| sx = s / √n |
3.461433 | 3.5 |
Use the following formulas:
| standard deviation | s = R . kn |
| relative standard deviation | sr = (s / x)
. 100 [%] |
| standard deviation of the mean | sx =
s / √n |
R - range of variation ==> R = xmax - xmin
kn - coefficient (see Table kn)
n - size of sample (No of measurements), in this case n =
5
x - arithmetic mean
Table kn values
n |
3 |
4 |
5 |
6 |
7 |
kn |
0.591 |
0.486 |
0.430 |
0.395 |
0.370 |
Example:
measured values xi |
round | |
| x1 | 74 | |
| x2 | 77 | |
| x3 | 91 | |
| x4 | 73 | |
| x5 | 81 | |
| arithmetic mean x | 79 | 79 |
| R = xmax - xmin = | 18 | |
| kn = | 0.430 | |
| s = R . kn = | 7.74 | 7.7 |
| sr= (s / x) . 100 [%] = | 9.772727 | 9.8 [%] |
| sx = s / √n |
3.461433 | 3.5 |