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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percentile calculation on group of data?

So I know how to calculate percentile on a simple data set: lets say student grades are 38, 47, 49, 58, 60, 65, 70, 79, 80, 92 Number of scores below 70 = 6 Using the percentile formula, Percentile = ...
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Interpretation of Value at Risk and its relationship with the upper percentile

I found this definition of VaR (Value at Risk) in a paper: VaR is defined as the “possible maximum loss over a given holding period within a fixed confidence level”. That is, mathematically, VaR at ...
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Calculate $1^{st}$ and last percentile without sorting data

Is there a method of calculating percentiles (even approximately) without sorting data? I have a lot of data points and I need to find rough min and max values, while ignoring some spikes in the data, ...
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Percentile of a discrete distribution with degenerate scores

I have a ranked dataset of 100 entries, where 10 entries have score 1 and 90 have score 0. How to interpret the first percentile of this dataset? Does this consist of the 10 entries with score 1? If ...
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Understanding the notion of percentiles [closed]

I want to preface this by saying I am a beginner in probability. I recently began reading the book "Algorithms to Live By", and so have been thinking about the optimal stopping problems for ...
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How to interpret covariance(A,B) divided by percentile rank of std dev(A)?

Is there a way to make meaning of it? I was thinking that maybe because the covariance is divided by the percentile rank of std dev of A, the magnitude of A is to a degree bounded. But how does it ...
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Inequality of tail probabilities for to distributions of the same parametric family?

Suppose $f(X,v_i), \textrm{ for } i=1,2$ are two probability distributions of the same parametric family. Moreover, I have a function L such that: $$\sum_{x} I_{\{L(X)\leq \bar{\gamma}\}} f(X,v_1) \...
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Alternative to the (log)normal distribution that allows for fitting percentiles

For the future development of a financial series, I have been given expected returns, volatility, and two percentiles (25th and 75th). Without the two percentiles given, I would choose to model the ...
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Ratio of the distance of two percentiles

Consider two sample means $\bar{X_1}$ and $\bar{X_2}$ from the same normal population having mean $\mu$ and standard deviation $\sigma$. The first sample mean is based on $n_1 = 10^k$ observations, ...
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Determining the Sample Standard Deviation

Suppose the brain volume for adult women is about 1,100 cc, with a standard deviation of 75 cc. Then consider a sample of 144 random women taken from this population, with an unspecified sample mean. ...
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Probability of a random sample lying between the mean and one standard deviation?

Is this a correct way of calculating the probability $P$ of a randomly selected sample from a distribution lying between the mean $\mu$ and the mean + standard deviation $\mu + \sigma$? Let the ...
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Question regarding extremities in Boxplots.

The minimum is mentioned as Q1-1.5IQR. Q1 is 25th percentile, and 1.5IQR is 75%. So how does the minimum work when Q1-1.5*IQR should be (-25th) percentile.
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How to calculate percentil from percentil subresults

I would like to calculate the 90th percentile, for example p90 for this dataset: p90(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) = 9.1 ...
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Can you calculate (or estimate) standard deviation using mean, median, and sample size? [closed]

If you know the mean, median and sample size (with no other information), can you estimate standard deviation? Or, let's say you know one value from the sample (only 1), can you tell which percentile ...
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How to calculate percentiles in a triangle

i have this PDF function and i am tasked with finding the 20th percentile of X for Y = 2 where X is a random variable I tried calculating the area of the triangle for x=0.25 and it resulted in the ...
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Percentile Rank and Percentile

I was watching the video here. For an $n$ object numeric list, consider $x_{i}$ to be the $n$th value along its index. $\text{Percentile Rank of $x_i$}=\frac{\text{Number of Values Below } x_i}{n}\...
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How do I call mathematical object which is a group supporting multiplication by a number from R?

Suppose we have a group $G(T,+)$. It naturally supports "multiplication by an integer", e.g. $5 \cdot t = t + t + t + t + t$ for any $t \in T$. However, this can't be expanded to $Q$ or $R$: ...
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what does the data is within $0.5\sigma$ mean?

What does the data is within $0.5\sigma$ mean? I want to ask about a term about "this data is within $0.5\sigma$". If I understand correctly the person first calculates standard deviation($\...
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Finding percentile of normal distribution

We have two random variables, $X = N(2,9)$ and $Y = N(3,16)$ I'm tasked to compute the $25\%$ percentile of $T = X + Y$ I have a table of my normal distributed random variable $Z$ and as such, I was ...
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Calculating quartiles of a given PDF

I am supposed to calculate the quartiles ( 25th, 50th, 75th percentile ) of the PDF - f(x) = x*( 2 - e^(-2) ) if 0 < x < 1 f(x) = e^(-2x) if x ≥ 1 How should I go about ...
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75 percentile: find top offenders

Imagine that a car company wants to analyze all those orders late, yet to be delivered to customers. By late I mean that, to date, the contractual delivery date has expired. ID simply refers to the i-...
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MLE and confidence interval of $\tau$ where $P(X < \tau) = 0.98$

Let $X_1,...,X_n \sim N(u; \sigma)$ Let $\tau$ be the .98 percentile, i.e. $P(X < \tau )$ = 0.98: Find the MLE of $\tau$: Find an expression for an approximate $1 - \alpha$ confidence interval for ...
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Percentiles of sums of random variables

Heads up, I'm asking this question after having read Percentile of sum of random variables and other questions. Please don't close this as a duplicate. It's not the same question. Suppose I have two ...
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How to get value of X to come up with a pre-defined target percentage

My title would be off, so I'll try to explain it as clear as I can. Say I bought StockX at the price of X apiece. == DURING BUYING == Let X = 10 as Unit Price of StockX ...
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Simple Question About Percentiles

An automobile insurance company issues a one-year policy with a deductible of $500$. The probability is $0.8$ that the insured automobile has no accident and $0.0$ that the automobile has more than ...
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Ranking of value based on given quartiles of a range

May be a noob question here, but my query is: I have a range of values of which I have quantile values: example: q = [-10, 0.25, 0.5, 0.75, 10] I have a score value say .85 which i wish to rank but ...
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Simple question about difference in percentiles -- what's wrong with my solution?

An insurer's annual weather-related loss, X, is a random variable with density function $$f(x) = \frac{2.5(200)^{2.5}}{x^{3.5}} \qquad \text{for } x > 200$$ and $f(x) = 0$ otherwise. Calculate the ...
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What is the upper 100 alpha percentile for chi-square distribution and why use it?

Recently, I learned about the chi-square distribution.In my class I was told about the upper $100\alpha^{th}$ percentile $\chi^{2}_{\alpha}(k)$ and given the following definition: $$P(X<\chi^{2}_{\...
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Find percentile of Discrete Probability Distribution

This is just a hypothetical question that I had (I made this question myself, just am curious about something). What if we were trying to find the $20\text{th}$ percentile in a discrete probability ...
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Correct statistical method to test for a change in percentile (not mean)?

I want to test the impact of a process change on an operational metric, which is a continuous variable. I have two data sets, pre-test and post-test. Both data sets represent the entire population of ...
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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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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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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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Percentile of positive values of $\max(0,X-500)$ given the CDF of $X$

$X$ follows a distribution with distribution function $$F(x)=\begin{cases}1-\left(\frac{2000}{2000+x}\right): &x\ge0\\ 0: &\text{otherwise}\end{cases}$$ Let $Y=max(0,X-500)$. Calculate the $60^...
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Finding percentiles of the $\chi^2$ distribution [closed]

If the random variable $Y$ has a $\chi^2$ distribution with $54$ degrees of freedom, then what is the approximate $84^{\text{th}}$ percentile of $Y$? I don't understand very good question when it is ...
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Calculate the percentile correspond and the percentile of the sampling distribution

The SAT placement test for admission to American universities had an average of μ = 1026 and a standard deviation σ = 209. The distribution of marks is approximately normal. a) Ramon had a grade of ...
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Why does the 90th percentile come out to be greater than the greatest number?

Why is the 90th percentile of the following numbers 0.193204884? 0.193111065 0.188885706 0.191501273 0.193298704 0.18895934 0.192364606How can the 90th percentile be greater than the greatest number ...
navneesi's user avatar
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1 answer
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Given a number (17) between a range of numbers (14-21) or (minRange-maxRange) what is the formula to achieve an output of 0 - 1? [closed]

Given a number (17) between a range of numbers (14-21) or (minRange-maxRange) what is the formula to achieve an output of 0 - 1? So given a range of (14-21) with a number of 17.5 would achieve an ...
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GRE Quantitative Reasoning Percentile Problem

The population of a city A in 2012, consisted of 45% men, 35% women and the remaining children. Of the children, 40% were female and 60% male. Of the men, 10% were over the age of 60 years and 25% ...
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Are the first and third quartiles exactly equal to the median of the lower and upper halves of the data?

Suppose I have a set of quantitative data $x_i$, with $1 \le i \le N$. This set has a median $M = x_m$, where the median $M=x_m$ where $m=\frac{N+1}{2}$ if $N$ is odd, or $M=\frac{x_\mu + x_{\mu+1}}{2}...
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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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