Question

Data on the compressive strength of a concrete block after testing are as follows: 2.50 MPa, 2.55 MPa, 2.52 MPa, 2.51 MPa, and 2.56 MPa. Find the absolute uncertainty.

Answer 1

First, find the deviation of each value from the average value $\mu$:

$$\mu=\frac{2.50 + 2.55 +2.52 +2.51 + 2.56}{5}=2.53\text{ MPa}.$$

Find the deviations:

$\delta_1=|\mu-x_1|=2.53-2.50=0.03\text{ MPa},\\ \delta_2=|\mu-x_2|=|2.53-2.55|=0.02\text{ MPa},\\ \delta_3=0.01\text{ MPa},\\ \delta_4=0.02\text{ MPa},\\ \delta_5=0.03\text{ MPa}.$

The absolute uncertainty is

$$\delta=\frac{\sum^n_{i=1}\delta_i}{n}=\frac{0.03+0.02+0.01+0.02+0.03}{5}=0.02\text{ MPa}.$$