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Questions tagged [quantiles]

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles. Quantiles are used in quantile-normal and quantile-quantile plots, which can be useful for examining the shape of distributions.

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Can the 90th percentiles of two sub populations both be lower than the overall?

Consider two populations, $A$ and $B$. $A + B = C$. Meaning $A$ and $B$ are mutually exclusive and collectively exhaustive of $C$. Given the above if I calculate the 90th percentile of some metric for all populations is it possible that $P90_C \ge…
sedavidw
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Compute quantile of sum of distributions from particular quantiles

Let's assume $N$ independent random variables $X_1, ..., X_N$ for which the quantiles at some specific level $\alpha$ are known through estimation from data: $\alpha = P(X_1 < q_1)$, ..., $\alpha = P(X_N < q_N)$. Now let's define the random variable…
albarji
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$\min(x)$ as a quantile estimator for the 1% quantile of $x$

I have recently found the following quantile estimator for a continuous random variable in a (nonstatistical, applied) paper: for a 100-long vector $x$, the 1% quantile is estimated with $\min(x)$. Here is how it performs: below is a kernel density…
Richard Hardy
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25th and 75th percentile according to wolfram alpha

I'm just studying my statistics exams and I came across something odd. When I try to get the 25th or 75th percentile with wolfram alpha, it gives me another answer than I should get according to my textbooks. simple example:…
zeta
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Is there any advantage of fitting a distribution to the data to calculate the percentile?

Method 1: Calculating the percentiles, e.g. 99 percentile of the data, is straight forward, and the calculation is based on the ordering of the data values. Method 2: A more complicated way of calculating the percentiles will be first fit a…
Michael
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What is the closest approximation to computing the $X$th percentile (say 95th) from bins of data?

I have a few bins of data. From each bin(which has a few thousand data points), I can compute the total number of data points, the mean of the data points, etc.. I can probably compute any/most statistical entities(mean, median, etc.) of each…
Vijay Kotari
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How to calculate a percentile of y for a given x given a series of (x, y)?

I have a scatter plot of (for example) height against age. How does one calculate for an individual point the percentile of the height for a given age? Suggestions in R would be most appreciated. Thanks!
Andrew
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How to calculate quartiles and other percentiles?

Given the following data: 972, 975, 985, 993, 993, 995, 998, 1001, 1004, 1007, 1008, 1009, 1011, 1015, 1016, 1020, 1022, 1032 I calculate the lower quartile as follows: Number of values: 18, Number of 'gaps': 17. Lower quartile is at 17/4 + 1 =…
fractor
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Percentile calculation for the combined group

I was struggling to find some solution of my problem which is as below: Let say, I have 20 groups and for each group I have say 10the percentile value. Then is it anyway possible to calculate the 10th percentile for the combined group using those 20…
Saptarshi
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Definition of quantiles (e.g., decile, quintile)

The field of research I'm in uses ranked data a lot. We often refer to deciles to mean the group of units that make up one-tenth of a population or sample. Recently I saw a paper which made the point that the word deciles should be used to refer to…
Bradford
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Are there two different possible meanings for a quantile group?

I'm aware that when a quantile is mentioned, it may mean a point or it may mean a group. But i'm not asking about the quantile points. In the case where it means a group, then there seem to be two meanings.. I'd like to confirm that there are these…
barlop
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Upper and lower quantiles

I have a question regarding upper and lower quantiles. In my lecture notes these are defined as: $Q_p[X] = \inf\{x \mid P(X \leq x) \geq p\}$ is the lower p-quantile $Q^p[X] = \inf\{x \mid P(X \leq x) > p\}$ is the upper p-quantile For which…
user1970122
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Would this Normal Quantile Plot be considered normal?

How would I describe this QQ plot? Would it indicate fair normality? Or would it be skewed? I have attached the histogram also. I have been asked to the answer the following: "By referring to the normal quantile plot below briefly discuss if the…
Jaime
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Compare value with distribution

I have developed a model that returns flight times between two airports e.g. Paris Rome, 115 minutes. I would like to compare this value with the value distribution from real flights e.g. (123, 110, 130, 120, 111, ...) My model calculates time for…
Francisco Lemos
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I have data on income for two groups, but the income is in deciles - how can I compare them?

The income data is in interval format. The data does not have individual income measurements. But is in {1,2...10}, that is in deciles, where 1 is the lowest income range and 10 is the highest. What are the common ways I can compare the income…
Thomas Veale
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