# Measurement and result interpretation

Discussion in 'General Electronics Chat' started by fila, Sep 13, 2012.

1. ### fila Thread Starter Member

Feb 14, 2011
64
5
I would like to know how to interpret the results of a measurement. Suppose you are designing a circuit. At point A in the circuit the voltage must have a value $x_0$.
You build the circuit and take N measurements $(x_1, x_2, ..., x_N)$ at that point and obtain the average value $x_{avg}$.

Now we have to analyze the result. First we calculate the (absolute) difference between the desired value and the measured value

$|{\Delta}x| = |x_0 - x_{avg}|$.

That gives us some information about the quality of the design. But that isn't good enough.

Let's say that $x_0$ = 5 V and $x_{avg}$ = 4.9 V. We calculate |Δx| = 0.1 V. Another example is $x_0$ = 0.2 V, $x_{avg}$ = 0.1 V gives also |Δx| = 0.1 V.

But now if we calculate the relative difference

$x_{relative} = \frac{|{\Delta}x|}{x_0}$

the first example gives us $x_{relative}$ = 2 %, and the second example $x_{relative}$ = 50 %.

Based on these examples how would you interpret the results? Are there any general rules or standards in the world of electronics about these values (absolute difference, relative difference)?

2. ### #12 Expert

Nov 30, 2010
18,082
9,646
In electronics, the % difference from the intended is usually the important number.

1-(dX/Xo) x100= % error

3. ### fila Thread Starter Member

Feb 14, 2011
64
5
How small would it have to be (error) to conclude that the design is good?

4. ### #12 Expert

Nov 30, 2010
18,082
9,646
Depends on your goal. I used to work 1% meters. For that, "good" was less than 1%.
In early TV's, 20% was often considered good enough.

5. ### Papabravo Expert

Feb 24, 2006
11,735
2,483
If you compute the variance of the samples it will tell you the range of likely values with high probability. The square root of the variance is the standard deviation. 99% of all the measurements will be within 3 standard deviations of the mean. If you establish what you expect that range to be and the measurements confirm that, then you have some evidence for calling it good.

6. ### Moon968 New Member

Apr 14, 2014
10
0
To achieve the most exact results possible and to identify measurement errors multiple readings are unavoidable.