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For example, consider the 1 MΩ resistor (1000 KΩ), the topmost entry. The tolerance arrows are at 95% and 105%, since this is a 5% part. The red circle is at approximately 109%, indicating measured mean of all similar value parts is 9% high. Since 9% high is outside the ±5% tolerance, the red circle is not within the blue arrow tolerance bounds.

One additional point is that there seems to be little difference between 5% and 10% parts—both seem to have aged about the same amount. This suggests there was no difference in construction, but rather parts were sorted by value into 5% and 10% groups. (If so, this means that 10% resistors will likely be devoid of parts around the nominal value, as they were removed and sold as 5% tolerance parts.)

I did not compute the standard deviation, because I entered the data by hand and it was too burdensome to compute the higher order statistical parameters. However, I did discard a couple of resistors that were clearly bad, e.g, a 3.3 KΩ part measured 4.2 KΩ.

Let's look, however, at the distribution pattern for 39 KΩ and 820 KΩ parts. I selected these because there were enough parts (12 and 10, respectively) to provide a moderately meaningful distribution.
 

The 39 KΩ is a 5% part, so the highest in-tolerance value allowed is 40.95 KΩ, and none of the parts measured within that tolerance. The 820 KΩ resistor is a 10% part, so the highest in-tolerance value is 902 KΩ, and we see seven of the 10 parts were in tolerance, with three out.

None of these resistors have been used in equipment, so the changed values are due to normal aging. (At least I assume the parts were in tolerance when new. They are manufactured by one of the major component houses in business at the time and are physically appear new.) It's well known that carbon composition resistors drift up in value with age, and that drift is accelerated by heat.

The lesson to be learned from this is that some parts—carbon composition resistors in particular—do not age well, and if you decide to keep these around the shack for historical restoration, by all means check their values before installing.

I'll also mention in passing that I have a variety of 1% metal film resistors of similar vintage and all check within the 1% tolerance. Carbon composition resistors are notoriously unstable, and the modern carbon film and metal film parts are much better in terms of long term stability, temperature stability and being within tolerance. It's rare, at least in my experience, to measure a 5% tolerance carbon film resistor and find it more than 2% or 3% from nominal value.