# What are the 10th percentile and z-score for a set of eye measurements?

• n77ler
In summary, the 10th percentile of the measurements for the eyes of 100 university students was 2.5. The z-score for the measurement of 1.07 was 0.0366.
n77ler

## Homework Statement

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.

## Homework Equations

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

## 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 doesn't it? when the number is much bigger(or the outlier) than the rest of the data?

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

opps is it supposed to be the deviation on bottom?

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.

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)

Last edited:
My textbook shows the denominator as 's' which is the standard deviation? And that's it , nothing else.

## 1. What is the difference between percentiles and z-scores?

Percentiles and z-scores are two different ways of measuring a data point's position in a distribution. Percentiles represent the percentage of data points that fall below a given value, while z-scores represent the number of standard deviations a data point is from the mean of the distribution.

## 2. How do you calculate percentiles and z-scores?

To calculate a percentile, you must first arrange the data in ascending order and then determine the data point's rank in the distribution. This rank is then divided by the total number of data points and multiplied by 100 to get the percentile. To calculate a z-score, you subtract the mean from the data point and divide by the standard deviation.

## 3. What is the significance of percentiles and z-scores?

Percentiles and z-scores are important in statistics as they allow us to compare and interpret data points in a distribution. They also help us identify outliers or extreme data points that may skew the overall results.

## 4. Can percentiles and z-scores be used interchangeably?

No, percentiles and z-scores cannot be used interchangeably. They represent different measures and have different interpretations. While percentiles give the position of a data point in a distribution, z-scores give a standardized value that can be used to compare data points from different distributions.

## 5. How are percentiles and z-scores used in real-world applications?

Percentiles and z-scores are commonly used in fields such as education, finance, and healthcare to analyze and compare data. For example, in education, percentiles and z-scores can be used to evaluate a student's performance in a standardized test compared to their peers. In finance, z-scores can be used to assess the risk of a particular investment. In healthcare, percentiles and z-scores can be used to track the growth and development of children.

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