# Percentiles and z-scores

1. Sep 16, 2008

### n77ler

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

The following 25 measurements were obtained on the eyes of over 100 university students.
0.04 0.06 0.06 0.06 0.07 0.07 0.08 0.08 0.09 0.09 0.09 0.10 0.11 0.12 0.12 0.15 0.16 0.16 0.16 0.17 0.17 0.17 0.20 0.21 1.07

a) Find the 10th percentile of these measurements. Interpret the result
b)Calculate the z-score for the measurement of 1.07. Interpret the result.

2. Relevant equations

I= (P/100)n
P defined as percentile
n defined as #of measurements

3. The attempt at a solution

I= (10/100)25 = 2.5 Round up to 3. So the 10th percentile is the third value when rearranged from smallest to greatest. It ends up being the second 0.06 value in the set. So how do I write the final answer? Do I just circle the third value?
z-score needs mean. x(bar)= sum of all numbers/ number of measurements
mean= 0.1544
z-score= (1.07-0.1544)/25 = 0.0366 but this seems a little small for a z-score doesnt it? when the number is much bigger(or the outlier) than the rest of the data?

2. Sep 16, 2008

for the second problem - check your formula for a Z-score.

3. Sep 16, 2008

### n77ler

opps is it supposed to be the deviation on bottom?

4. Sep 16, 2008

### n77ler

Another little question. If I had a venn diagram and the two circles in it were labelled A and B and they weren't mutually exclusive and I was asked to give the probability of
A and B intersection but A is a complementation. I think it is 0 because there can only be values where the circles overlap and the complementation will have no values.

5. Sep 16, 2008

Re the Venn Diagram question: break your question down into sentences and write it more clearly because:
1. It isn't immediately clear to me what the core question is
For the $$Z$$-score question: look in your stat book, or notes, or both, for the definition of a sample $$Z$$-score - that will clarify the denominator. (word of advice: the denominator is neither the sample size alone nor the standard deviation alone)