Scatter, mean, deviation – what’s really behind your measurement data?
The most important statistical terms in surface testing – clearly explained, immediately applicable.
No measurement is perfect. Whether coating thickness, electrical conductivity, or material composition – every measurement fluctuates. Misinterpreting these fluctuations leads to poor decisions: rejecting good batches, accepting bad ones, or wasting time on unnecessary rework. The solution isn’t more individual measurements – it’s knowing how to work with statistical parameters. FISCHER devices deliver these analyses automatically – here we explain what the numbers actually mean.
What does the mean tell us – and what doesn’t it tell us?
The mean x̅ condenses a series of measurements into a single number: add up all the measured values and divide by the number of measurements. This is known as the arithmetic mean – by far the most commonly used method in practice.
Important: The mean alone says nothing about coating quality. Two measurement series can have the same mean and yet describe completely different coating qualities. That’s why you always need an additional measure of dispersion.
How can I tell how much my measurements are varying?
Range R: fast, but vulnerable
The range R is the difference between the largest and the smallest value in a measurement series. It can be calculated instantly and gives a first overview. However, it is extremely sensitive to outliers: a single faulty measurement can distort the range and lead to incorrect conclusions. For small samples it may suffice – for larger datasets, the standard deviation is the better choice.
Standard deviation σ: the reliable measure of dispersion
The standard deviation σ indicates how far individual measurements deviate from the mean on average. A high standard deviation means the values are widely scattered – the coating is uneven. A low standard deviation means the values cluster closely together – the coating process is reproducible.
The more measurement points available, the more meaningful the mean and standard deviation become together.
When does it make sense to compare different coatings?
This is where the coefficient of variation V comes in. The problem: a higher average coating thickness automatically produces a higher absolute standard deviation – even if the relative uniformity is exactly the same. The coefficient of variation solves this by dividing the standard deviation by the mean and expressing the result as a percentage.
This makes dispersion comparable regardless of absolute coating thickness – ideal for fairly evaluating coatings of different thicknesses or different production batches against each other.
Practical example: When identical standard deviations mean very different things
You measure two coatings: a thin layer averaging 10 μm and a thick layer averaging 100 μm. Both have a standard deviation of 1 μm.
At first glance this looks the same – but the coefficient of variation tells a different story: the thin coating has a V of 10 %, the thick coating only 1 %. The thin coating is therefore ten times less uniform in relative terms. Without the coefficient of variation, this difference would have remained invisible.
Another example: two measurement series [1 / 2 / 3] and [1.5 / 2 / 2.5] both have a mean of 2 – but standard deviations of 1 and 0.5 respectively. The second series is more uniform, even though the mean gives no indication of this.
A histogram shows how often certain values were measured. The red line shows the mean of the distribution, while the shaded area spans two standard deviations, i.e. about 68% of all the measured values.
The 4 key parameters at a glance
| What it tells you | |
|---|---|
| Mean x̅ | Representative average value of a measurement series |
| Range R | Gap between the smallest and largest value – simple, but vulnerable to outliers |
| Standard deviation σ | How strongly the measurements scatter around the mean – the central quality indicator |
| Coefficient of variation V | Relative dispersion in % – enables fair comparison of coatings with different thicknesses |
| Mean x̅ | Representative average value of a measurement series |
|---|---|
| Range R | Gap between the smallest and largest value – simple, but vulnerable to outliers |
| Standard deviation σ | How strongly the measurements scatter around the mean – the central quality indicator |
| Coefficient of variation V | Relative dispersion in % – enables fair comparison of coatings with different thicknesses |
Get the most out of your measurement data – we’re here to help.
Statistics are one thing – the right measuring device and software are another. Our specialists will advise you on FISCHER measurement solutions for coating thickness measurement, material analysis, and material testing, and show you how to optimize your evaluation workflows. Contact our specialists now!
