Measurements - Absolute vs. Relative Frequencies
Absolute and relative measurements to characterize and compare data sets.
Measurements are important in all production processes to achieve required quality.
A measurement data set can be like the weight samples of a product:
|
Sample | Sample Value - x - |
|---|---|
| 1 | 1.0 |
| 2 | 1.1 |
| 3 | 0.9 |
| 4 | 1.0 |
| 5 | 1.0 |
| 6 | 0.9 |
| 7 | 1.1 |
| 8 | 1.0 |
| 9 | 1.1 |
The absolute frequencies for the each measured value:
|
Sample Value | Absolute Frequency - h - |
|---|---|
| 0.9 | 2 |
| 1.0 | 4 |
| 1.1 | 3 |
The data set size corresponds to the number of samples and the total of the absolute frequencies:
n = h1 + h2 + .. + hk
= Σ hi (1 < i < k) (1)
where
n = no. samples
h = absolute frequency of sample measurement
The relative frequency can be expressed as
fi = hi / n (2)
where
fi = relative frequency of sample
Adding all relative frequencies produces value 1.
Σ fi = 1 (1 < i < k) (3)
The arithmetic mean (average value) can be calculated as
