Standard Deviation of Linear Dimensions P and Q

The standard deviation is a measure of the dispersion or variability of a set of data. In this case, we are given two linear dimensions, P and Q, and their respective standard deviations.

Given Information:
- Standard deviation of dimension P = 3 mm
- Standard deviation of dimension Q = 4 mm

To find the standard deviation of the resulting linear dimension (P + Q), we need to understand the concept of combining standard deviations.

Combining Standard Deviations:
When two dimensions are added or subtracted, their standard deviations are also added. This can be expressed mathematically as follows:

If X = P + Q, where P and Q are independent random variables, then the standard deviation of X, denoted as σ(X), is given by:

σ(X) = √(σ(P)^2 + σ(Q)^2)

Where:
- σ(X) is the standard deviation of X
- σ(P) is the standard deviation of P
- σ(Q) is the standard deviation of Q

Calculating the Standard Deviation of (P + Q):
Using the formula mentioned above, we can calculate the standard deviation of the resulting linear dimension:

σ(X) = √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5 mm

Therefore, the standard deviation of the resulting linear dimension (P + Q) is 5 mm.

Explanation:
When two linear dimensions are added or subtracted, their standard deviations are combined using the formula mentioned above. In this case, since we are adding two dimensions, their standard deviations are added as well. The resulting standard deviation represents the variability or dispersion of the combined dimension. In our calculations, the standard deviation of dimension P is 3 mm and the standard deviation of dimension Q is 4 mm. By applying the formula, we find that the standard deviation of the resulting linear dimension (P + Q) is 5 mm. This means that the combined dimension is expected to vary or deviate by approximately 5 mm from the mean.