Random Uncertainty

Your friend asks you to measure their height. You use a tape measure (with centimeter markings) and get 180 cm. Your friend asks you to quantify how accurately you can determine their height. To answer this you decide to ask two more people to measure your friend's height. You record these multiple trials of the height measurement in a table.

Trial	Height (cm)
1	180 cm
2	179 cm
3	182 cm
Average	180 cm

You realize that by doing multiple trials and finding the average you've estimated the height, and gotten a sense of how accurately you've measured. Trial 3 is furthest from the average, 182 cm - 180 cm = 2 cm from the average to be precise. One way of quantifying the random uncertainty of the measurement is to quantify the range of measurements. The complete statement of the measurement of your friend's height is 180 cm 2cm . This means your friend's height is in the range between 178 cm and 182 cm .

There is no way to measure your friend's height exactly. There's no way to make any measurement exactly. Every measurement has uncertainty. The first step to estimating uncertainty is to do multiple trials of the measurement. Doing multiple trials doesn't determine the uncertainty in a measurement, it only estimates it. If you want to estimate the uncertainty better you can do even more trials. You find one more person measure your friend's height.

Trial	Height (cm)
1	180 cm
2	179 cm
3	182 cm
4	184 cm

1. What is the new average, in cm?

2. What is the new random uncertainty from the previous question, in cm?