Question

Consider repeated timings of 50 swings of pendulum to be 23.8, 23.5, 23.7, 23.4 seconds. Calculate the standard error in the measurement.

Answer 1

Find the average value:

$$a=\frac{23.8+ 23.5+ 23.7+ 23.4}{4}=23.6\text{ s}.$$

Determine the standard deviation:

$$\sigma=\sqrt{\frac{(23.6-23.8)^2+(23.6-23.5)^2+(23.6-23.7)^2+(23.6-23.4)^2}{4-1}},\\\space\\ \sigma=15.7\text{ s}.$$

Calculate the standard error:

$$\sigma_x=\sigma/\sqrt n=7.85\text{ s}.$$