# Questions tagged [percentile]

A value representing the lowest $n$ percent of the values in a data set or of the possible values of a random variable.

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### $z$ - score to percentile using normal distribution or linear scale

I am stuck on a problem. I have a list of $z-$ score for a list of companies, I would like to convert that $z-$ score to a percentile / $0-100$ scale. I currently have 2 ways in mind on how to do this:...
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### Notation for a set of quantiles

Is there a formal notation for a set of quantiles of for instance x, a numerical array? This answer suggests the notation for percentile is Pi (though what to do if you already have a variable P is ...
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### Estimation of the percentile 0.85. [closed]

Let $X_{1},...,X_{n}$ be independent random variables with exponential distribution of parameter $\lambda$. The task is to find the maximum likelihood estimator and the first moment estimator of the ...
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### Estimating probability of experiencing 100th percentile: is this a valid approach?

Say you work on a website. When someone accesses the website in their browser, then the website makes 5 more calls to different services to load the remaining content. The issue is, until all content ...
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### On describing percentiles within quartiles

In describing the relationship between percentiles and quartiles of a data set, is it accurate to say that the percentiles belonging to the first quartile range from the zeroth to the 24th percentile? ...
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### percentile rank formula vs excel

Given following set of data I expect percentile rank of 38 to be 50. 21, 21, 29, 31, 35, 37, 37, 38, 38, 38, 39, 41, 43, 43, 48, 48, 50, 54, 64, 73 number of scores <= 38 / length * 100. But using ...
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### Multi conditional probability question

I am throwing one red, one blue and one yellow ball on a grid type table and log each trial. I log the distance of red and blue balls to the yellow one. After 100 trial, i have a historical data and ...
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### How do you pronounce 0.1st percentile?

I'm analyzing some out of range values that are either really high (above the 99.9th percentile) or really low (below the 0.1st percentile). How would you pronounce 0.1st percentile?
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### Calculating Percentiles on a large and constantly changing set

Background: Let S be a set of scores. These scores can be any positive real number. The size of S is large. A specific score s is subject to change frequently. I would like to tell each user (a user ...
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### Is there a formula to assign a 0 to 5 score by comparing your value against the min and the max of a range?

Lets say I have a database of customers with how much they spent so something like Jim 100 Bob 300 Tim 14 Sarah 43 Rob 945 Jake 3,000 etc What I want to do is then assign each customer a ...
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### How do I find the percentile of a distribution with information only about mean, variance, skewness and kurtosis? [closed]

e.g., if my data distribution has 4 points, with a mean of 5, skewness 13, kurtosis 220 and variance 11, how do I find the 75th percentile? Or is this example a very special case?
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### Ambiguity between methods of calculating quartiles. Which method is more correct? [duplicate]

I am having confusion between two methods of calculating the first quartiles. Let me explain by an example: $A = [1,2,3,4,5]$ The method that I know: To find the first quartile in the list above I ...
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### How to calculate lower percentiles (10th, 25th, 40th, etc.) given the 50th percentile and a bunch of upper ones?

I have a data set that has data for the 50th, 60th, 70th, 75th, 80th, 85th, 90th, and 95th percentiles. I am trying to figure out how I should go about calculating the lower percentiles I need (10, ...
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### How to find the $60$th percentile of pdf?

The pdf of $x$ is $f(x) = .1$ with the interval $3 < x < 13$ This problem requires me to find the $60$th percentile. I assume that I need to solve for the interval from $3$ to $13$ of this ...
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### How to get a probability function from percentiles, average, etc.?

I have the average, minimum, maximum and p50, p90 and p99 percentiles about the time to takes a website to return an answer. Anyway, I can get other percentiles, like p10, p20, p30, etc. How can I ...
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### How does mathematical software, like Libreoffice Calc, manage to find percentiles when there are no any in the first place?

From now on I will say "exclusive percentile" to refer to a percentile defined by the exclusive definition of percentiles. Similar goes for "inclusive percentile". Look at this screenshot: We have ...
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### Proofs that the median and a 50th percentile aren't always the same thing. Is my reasoning correct?

For our purposes we need to find at the least one case when a 50th percentile and the median aren't the same thing. I will present three such cases. Here the first case (proof) goes as this: Suppose ...
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### Is it true that for some datasets certain percentiles don't exist?

Here is my reasoning: Let's assume the exclusive definition of a percentile here. Suppose we have a set of numbers {10,20,30,40} and we want to calculate value of its 90th percentile. But such value ...
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### Does the 0th percentile exist?

For me it seems that it does. Here is my reasoning, please correct me if I'm wrong: We have 3 definitions of a percentile, let's check if the 0th exists for each of them. The exclusive definition: ...
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### Empirical Rule percentile?

Back again! This is probably simple, but I also wanted to check my answer, so here is the question: The distribution of heights of adult American men is approximately normal with a mean 69 inches and ...
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### Variation of percentile value of a set of data after normalization

I have a theoretical question. Given a set of data, whose 95th percentile is X: If I normalize the data, doing zscore normalization, i.e. (data-mean)/std, is the 95th percentile of the normalized ...
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### What Conclusions Can I Draw from Percentiles About my Set of Data?

I have a specific survey question that I am analyzing for the topic Should High Schools Implement a Uniform Policy?. I am supposed to create biased survey questions ...
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### Understanding percentile computation

I understand percentile in the context of test scores with many examples (eg. you SAT score falls in the 99th percentile), but I am not sure I understand percentile in the following context and what ...
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### What Can Median Tell Me About my Data?

For a final assignment for math, I was required to take the "Yes!" side of 'Should Uniforms Be Implemented at School?' My job was to create a biased survey that would make people agree with our side ...
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### Can You Have 2 Numerical, Identical Values To Represent the nth Percentile?

For an assignment, I am required to find the value of a piece of data in the 70th percentile using mean and standard deviation. Here is my organized data in ascending order: ...
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### Calculate percentile rank

I am confused with the concept of percentile rank. I am in the top 7 of my class, how would I calculate my percentile rank? Number of students 72 I am 7th rank in my class Does this mean my ...
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### Conventional notation for quartiles of probability distributions (not quartiles of samples)

EDIT: Should I better post this question in https://stats.stackexchange.com/?? NOTE: Here, I am supposing that the reader knows the difference between population (which is where a probability ...
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### Why do we use average of two numbers during calculation of percentile?

Let me give you example: The right answer is supposed to be (according to the book) "908". I see how we arrive to such number.(10*0.4=4, then we take the fourth film from the bottom, it's "Jaws". The ...
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### How to calculate Percentile of given value based on other values and percentile

I have a problem related to a formula and I need help from all of you. It may use some statistics formula to solve the problem. Your help would be appreciated. =========== We have following values (...
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### Calculate the value given several percentiles and their values

On a particular test whose scores are distributed normally, the 2nd percentile is 1,720, while the 84th percentile is 1,990. What score, rounded to the nearest 10, most closely corresponds to the 16th ...
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### Is there something like 700%?

I always see companies advertising their products as "700% effective " or "the product kills 900% germs". But percent means "out of hundred". So how can the percentage be more than 100 like 700% or ...
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### The 44th percentile is the .44th __?

I'm searching for a very simple word. We are all familiar with the concept of the 44th percentile of a real, random variable. In a sense, percentile (parameterized by the random variable) is a ...
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### How can I calculate desired selling price based on margin? [closed]

I use the following formula to calculate profit margin: $$\text{profit_margin} = \frac{\text{selling_price} - (0.15\cdot \text{selling_price}) - \text{sourcing_cost}}{\text{sourcing_cost}}$$ What ...
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### How can 10th (or any other sufficiently low) percentile be equal to the mean number?

For example, a 3rd percentile equal to n means that values of no more than 3% of observations in a group of observations are strictly less than n and that values of no less than 3% of observations are ...
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### When do mean value may be equal to some percentile? Let’s say 3rd percentile.

I started reading about statistics recently and saw that this question was asked several times during interviews.
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### Find the limit of a probabilistic matrix

I have the following matrix $M$, where the first column is a score vector and the second column is a vector with the corresponding probabilities:  M = \begin{pmatrix} 0 & \psi_0\\ 1 & \psi_1\...
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### Piecewise integration: find the 75th percentile of this continuous random variable.

The problem from a quiz of mine is as follows: In general, I know how to find the $p$th percentile of a random variable $X$, given its probability density function $f(x)$. You simply solve for the ...