How to use correctly the standard deviation for a sample? (object weighted 3 times during production)

Parcosan

New member
Hi everybody,

a composite object is weighted 3 times during 3 phases of its manufacturing process:
1. After object is trimmed
2. After object has filler applied
3. After object is painted
I recorded the measured weights of 10 samples and I calculated for each object the separated weight of filler and painting as difference of measured values:

Sample IDMeasured weight after trimming [g]Measured weight after filler [g]Calculated weight of filler [g]Measured weight after painting [g]Calculated weight of painting [g]
1251027102510-2710=20028302830-2710=120
2263027901602900110
3266029502903090140
4262028802602990110
5261027201102890170
626002992392306068
7267031705003300130
826602740802870130
9250027902902960170
10263028001702992192
Average260928542452988134
Standard Deviation59.34145.90129.63137.4336.10

Now my question:
Under the supposition that all data are Normal Distributed, if I would describe the statistical distribution of the variable "Weight of painted object", which of the following Standard Deviation should I use?
1. The value of the 5th column: 137.43
2. The Standard Deviation calculated as sum of Standard Deviations of: weight of object trimmed+weight of filler+weight of painting: $\sigma_{after-inting}=\sqrt{\sigma_{after-trimming}^2 + \sigma_{filler}^2+ \sigma_{painting}^2}=\sqrt{59.34^2+129.63^2+36.10^2}= \bold{\textcolor{red}{147.06}}$
Thank you for any suggestion/comment,

Parcosan

Last edited:
I would say the first one.

Your first calculation, 2510-2710=200, is wrong.

My problem in using the first formula is that the filler quantity applied and the painting quantity applied, are not depending from the first variable of object weight.
This means that the values of column filler weight can be also mixed, and the same can be for painting weight.
In case you mix those values, the first formula will give you a different value of standard deviation, while the second formula will always remain the same.

Just to simplify, take the following 2 samples:

After TrimFillerPaintingAfter Painting
22001501202470
21002001702470

If you apply the first formula you will have a standard deviation of zero.
If you apply the second formula, you will have a standard deviation different from zero.
In my opinion when we sum the weight we loose some information.