# Statistics - standard deviations, etc

1. Aug 12, 2010

### joriarty

Statistics. The bane of my existence... and then a bit of statistics "revision" rears its (in my opinion) ugly head in my quantum physics course and I have absolutely no idea what to do.

1. The problem statement, all variables and given/known data

1. Suppose you measure the height of all students at the University. You use a ruler which is only accurate to ±0.5 cm (perhaps varies with temperature, stretches, numbers hard to read – whatever).

(a) On a given measurement you record 172.0cm. What range of values would you expect to get if you repeated this measurement several times?

(b) Make a sketch of the distribution of a sample of about 20 measurements of this particular student.

(c) Suppose your result after measuring all students is (height)=162.7±15.3cm. How much of the
15.3 cm uncertainty is due to your ruler?

(d) What fraction of students are taller than 162.7cm?

(e) What fraction of students are taller than 178.0cm?

2. Relevant equations

σ2 = ⟨x2⟩ - ⟨x⟩2

3. The attempt at a solution

I don't really know where to start. It's over 3 years since I did any stats at school. All I can understand is that standard deviation (σ) is some measure of average error over a range of samples. I haven't been given a range of samples, all I know is the uncertainty of ± 0.5 cm. For the first question, the student might be 171.5 cm tall, and the 172 cm measured is at the far end of this uncertainty. How can I come up with an expected range of values if this measurement was repeated?

2. Aug 12, 2010

### lanedance

you could write each measurement (Mi) as the sum of 2 random variables are error (Ei), and the heights (Xi) you :

$$M_i = X_i + Ei$$
then calculate the average & variance of N measurements assuming everything is independent