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

[Parcosan]

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 ID	Measured weight after trimming [g]	Measured weight after filler [g]	Calculated weight of filler [g]	Measured weight after painting [g]	Calculated weight of painting [g]
1	2510	2710	2510-2710=200	2830	2830-2710=120
2	2630	2790	160	2900	110
3	2660	2950	290	3090	140
4	2620	2880	260	2990	110
5	2610	2720	110	2890	170
6	2600	2992	392	3060	68
7	2670	3170	500	3300	130
8	2660	2740	80	2870	130
9	2500	2790	290	2960	170
10	2630	2800	170	2992	192
Average	2609	2854	245	2988	134
Standard Deviation	59.34	145.90	129.63	137.43	36.10

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: [math]\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}}[/math]

Thank you for any suggestion/comment,

Parcosan

 

[Harry_the_cat]

I would say the first one.

 

[Steven G]

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

 

[Parcosan]

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 Trim	Filler	Painting	After Painting
2200	150	120	2470
2100	200	170	2470

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.