Meta tags:
Headings (most frequently used words):
the, method, variant, percentile, contents, definitions, in, normal, distribution, applications, calculation, methods, see, also, notes, references, nearest, rank, cdf, linear, interpolation, between, closest, ranks, weighted, first, second, third,
Text of the page (most frequently used words):
the (215), percentile (65), displaystyle (63), and (53), for (44), statistics (26), rank (26), distribution (24), frac (24), score (23), that (20), #methods (19), are (19), this (18), function (18), method (18), data (18), edit (18), 100 (16), value (16), scores (16), analysis (15), text (14), percentiles (14), from (13), test (13), model (13), statistical (13), one (13), which (13), given (13), median (12), left (12), right (12), standard (11), sample (11), exclusive (11), nearest (11), regression (10), linear (10), time (9), normal (9), plot (9), definition (9), than (9), percentage (9), variant (9), inclusive (9), retrieved (8), correlation (8), ordered (8), way (8), also (8), cases (8), list (8), wikipedia (7), using (7), inc (7), with (7), limit (7), transformation (7), chart (7), range (7), weighted (7), between (7), ldots (7), interpolation (7), below (7), table (6), may (6), use (6), page (6), population (6), estimator (6), first (6), statistic (6), interval (6), mean (6), example (6), excel (6), there (6), can (6), leq (6), ranks (6), cdf (6), calculated (6), often (6), about (5), original (5), applications (5), log (5), likelihood (5), least (5), estimation (5), general (5), multivariate (5), variance (5), size (5), pdf (5), speed (5), above (5), values (5), number (5), begin (5), end (5), exc (5), version (5), second (5), not (5), three (5), forall (5), mod (5), used (5), 50th (5), interpolated (5), very (5), infinity (5), contents (4), search (4), models (4), survival (4), box (4), tests (4), anova (4), generalized (4), bayesian (4), alternative (4), power (4), experiment (4), normalization (4), deviation (4), 2013 (4), equal (4), see (4), when (4), then (4), where (4), inverse (4), result (4), lfloor (4), rfloor (4), will (4), such (4), algorithms (4), specified (4), either (4), main (4), calculation (4), sigma (4), hide (4), move (4), sidebar (4), toggle (3), view (3), under (3), additional (3), terms (3), was (3), summary (3), index (3), portal (3), control (3), design (3), engineering (3), product (3), squares (3), cross (3), partial (3), exponential (3), series (3), factor (3), adaptive (3), maximum (3), probability (3), inference (3), sum (3), parametric (3), unbiased (3), theorem (3), minimum (3), moments (3), point (3), family (3), shape (3), order (3), natural (3), study (3), scatter (3), fan (3), continuous (3), 2006 (3), doi (3), nist (3), software (3), limits (3), 85th (3), isbn (3), greater (3), called (3), known (3), positive (3), weight (3), region (3), microsoft (3), however (3), third (3), note (3), relationship (3), variants (3), therefore (3), each (3), corresponding (3), two (3), percent (3), represent (3), part (3), its (3), calculating (3), many (3), times (3), same (3), ordinal (3), less (3), return (3), shows (3), loscore (3), results (3), found (3), other (3), bandwidth (3), represents (3), related (3), rule (3), deviations (3), dark (3), blue (3), account (3), all (3), definitions (3), approximates (3), expressed (3), quartile (3), tools (3), topic (2), languages (2), contact (2), privacy (2), policy (2), non (2), commons (2), september (2), categories (2), articles (2), research (2), february (2), 2023 (2), short (2), description (2), different (2), wikidata (2), org (2), mathematics (2), information (2), system (2), national (2), accounts (2), reliability (2), epidemiology (2), studies (2), clinical (2), spectral (2), density (2), frequency (2), domain (2), autoregressive (2), vector (2), specific (2), structural (2), seasonal (2), adjustment (2), stationarity (2), distributions (2), cluster (2), principal (2), contingency (2), categorical (2), freedom (2), nonparametric (2), simple (2), equations (2), validation (2), coefficient (2), determination (2), pearson (2), moment (2), posterior (2), lehmann (2), most (2), bootstrap (2), confidence (2), distance (2), optimal (2), location (2), scale (2), empirical (2), sampling (2), theory (2), designs (2), trial (2), randomized (2), controlled (2), random (2), error (2), missing (2), reduction (2), cleaning (2), unit (2), scaling (2), transform (2), johnson (2), dispersion (2), geometric (2), arithmetic (2), outline (2), numpy (2), here (2), matlab (2), langford (2), education (2), elementary (2), 2021 (2), november (2), free (2), archived (2), 2018 (2), 2007 (2), 2011 (2), american (2), 2684934 (2), quantiles (2), packages (2), hyndman (2), 978 (2), references (2), contrast (2), notes (2), weights (2), formulas (2), taking (2), our (2), sorted (2), let (2), total (2), extends (2), restricted (2), narrower (2), means (2), suffix (2), indicates (2), both (2), whereas (2), would (2), only (2), source (2), some (2), including (2), noted (2), cap (2), mathbb (2), differ (2), should (2), produce (2), has (2), extreme (2), just (2), aligned (2), approaches (2), adjacent (2), uses (2), fractional (2), bmod (2), geq (2), rounding (2), closest (2), usual (2), lceil (2), rceil (2), but (2), 100th (2), computational (2), steps (2), difference (2), hiscore (2), hirank (2), lorank (2), although (2), they (2), set (2), section (2), learn (2), talk (2), assess (2), quantity (2), within (2), height (2), growth (2), 95th (2), top (2), peaks (2), usage (2), amount (2), internet (2), curve (2), thus (2), 13th (2), 87th (2), negative (2), lower (2), small (2), large (2), fall (2), human (2), observations (2), medium (2), cumulative (2), into (2), appearance (2), upload (2), file (2), changes (2), links (2), history (2), read (2), english (2), article (2), create (2), donate (2), menu (2), add, mobile, cookie, statement, developers, code, conduct, legal, safety, contacts, disclaimers, available, apply, site, you, agree, registered, trademark, profit, organization, wikimedia, foundation, creative, attribution, sharealike, license, rendered, parsoid, last, edited, 2026, utc, hidden, contain, percentages, https, php, title, oldid, 1373289841, wikiproject, category, kriging, geostatistics, geographic, environmental, cartography, spatial, psychometrics, official, jurimetrics, econometrics, demography, crime, census, actuarial, science, social, identification, quality, process, probabilistic, chemometrics, medical, trials, bioinformatics, biostatistics, nelson, aalen, hazard, hitting, accelerated, failure, aft, proportional, hazards, kaplan, meier, whittle, wavelet, fourier, autoregression, var, conditional, heteroskedasticity, arch, arima, jenkins, arma, xcf, pacf, autocorrelation, acf, breusch, godfrey, durbin, watson, ljung, johansen, dickey, fuller, granger, causality, break, cointegration, smoothing, trend, decomposition, elliptical, equation, classification, discriminant, canonical, components, manova, cochran, mantel, haenszel, mcnemar, graphical, cohen, kappa, degrees, covariance, partition, poisson, regressions, binomial, logistic, bernoulli, families, homoscedasticity, heteroscedasticity, robust, isotonic, semiparametric, nonlinear, predictors, ordinary, template, splines, mars, simultaneous, mixed, effects, errors, residuals, confounding, variable, bayes, credible, prior, van, der, waerden, jonckheere, terpstra, friedman, kruskal, wallis, mann, whitney, hodges, signed, wilcoxon, sign, bic, aic, selection, normality, shapiro, wilk, jarque, bera, lilliefors, anderson, darling, kolmogorov, smirnov, chi, squared, goodness, fit, student, wald, lagrange, multiplier, ratio, multiple, comparisons, randomization, permutation, uniformly, powerful, tails, testing, hypotheses, jackknife, resampling, tolerance, prediction, pivot, plug, scheffé, rao, blackwellization, estimators, estimating, frequentist, sensitivity, robustness, asymptotics, divergence, efficiency, loss, decision, functional, sufficiency, completeness, monotone, parameter, space, specification, quasi, sectional, cohort, observational, down, stochastic, approximation, scientific, assignment, interaction, factorial, blocking, experiments, questionnaire, opinion, poll, stratified, survey, methodology, replication, effect, collection, detrending, differencing, preprocessing, component, dimensionality, truncation, winsorizing, outlier, min, max, standardization, feature, fisher, anscombe, stabilizing, yeo, cox, transformations, processing, line, ecdf, matrix, heatmap, violin, stem, leaf, display, run, radar, pie, histogram, forest, correlogram, biplot, bar, graphics, spearman, kendall, dependence, grouped, tables, count, skewness, kurtosis, central, interquartile, variation, average, absolute, mode, lehmer, heinz, heronian, harmonic, cubic, contraharmonic, center, descriptive, 2017, scipy, documentation, equivalent, discussed, toolbox, 1080, 10691898, 11910589, journal, quartiles, 2009, handbook, wessa, office, development, louisiana, state, police, october, lsp, rational, robert, kuby, patricia, applied, going, flow, 10th, cengage, learning, 102, 9781111802493, schoonjans, bacquer, schmid, 751, 21811118, pmid, 3171208, pmc, 1097, ede, 0b013e318225c1de, 750, pottel, hans, flaws, lane, david, yanan, 1996, association, 365, jstor, 2307, 361, statistician, rob, couallier, vincent, gerville, réache, léo, huber, carol, catherine, limnios, nikolaos, mesbah, mounir, john, wiley, sons, 84821, 619, stephens, larry, mcgraw, hill, professional, 173647, schaum, engineers, typical, based, involving, because, includes, quantile, decile, cw_, suppose, have, associated, respectively, dots, addition, counted, instead, approach, primary, recommended, adopted, since, 2010, percentil, endpoints, does, fact, any, smaller, excluded, cause, excludes, property, hence, leftrightarrow, 100p_, furthermore, sources, prctile, near, margins, forced, absence, correspondence, wider, author, suggested, choice, sampled, tfrac, revised, now, degree, looking, like, 2c_, requirement, midpoint, occur, ways, constant, 100p, subscript, linearly, interpolating, nodes, integral, remainder, after, division, floor, simply, accomplished, doubling, leaves, unchanged, notin, calculate, described, odd, even, defined, largest, always, member, lists, fewer, distinct, being, more, corresponds, formula, texts, greatest, smallest, name, implies, programs, typically, functions, rounded, truncated, figure, illustrates, these, serves, introduction, examples, subsequently, simplest, compared, bit, crude, identified, nine, spreadsheet, describe, exists, interpolate, existing, material, how, remove, message, relevant, discussion, relate, verifiably, mention, possibly, contains, synthesis, finance, measure, dependent, portfolio, expected, sink, period, risk, traffic, road, guideline, setting, assessing, whether, too, high, low, physicians, infant, children, their, comparison, charts, bill, 98th, usually, cuts, off, month, bills, rate, infrequent, ignored, customer, charged, fairer, reason, useful, measuring, throughput, gives, accurate, picture, cost, says, remaining, burstable, service, providers, area, increasing, fixed, decimal, places, 28th, 72nd, 0th, falls, practical, upper, enforced, approximations, populations, following, represented, reference, plotted, along, axis, scaled, units, mathematically, proportion, individuals, outside, heights, few, people, level, representation, zone, side, light, yield, similar, formed, evaluated, seen, consequence, glivenko, cantelli, fraction, reporting, computed, were, determined, 90th, norm, referenced, input, refer, kilograms, pounds, infinite, measurement, type, obtained, subdivision, groups, 25th, p25, p50, 75th, p75, depending, denoted, approximately, 97th, p97, points, centile, divides, parts, analyzes, encyclopedia, item, projects, printable, download, print, export, switch, legacy, parser, get, shortened, url, cite, permanent, link, what, actions, اردو, українська, türkçe, ไทย, svenska, српски, srpski, русский, português, polski, norsk, bokmål, nederlands, 한국어, 日本語, italiano, עברית, galego, français, فارسی, euskara, español, deutsch, dansk, čeština, العربية, subsection, personal, special, pages, recent, community, help, contribute, current, events, navigation, jump, content,
Text of the page (random words):
similar results when the number of observations is very large and the probability distribution is continuous 6 in the limit as the sample size approaches infinity the 100 p th percentile 0 p 1 approximates the inverse of the cumulative distribution function cdf thus formed evaluated at p as p approximates the cdf this can be seen as a consequence of the glivenko cantelli theorem some methods for calculating the percentiles are given below in the normal distribution edit representation of the three sigma rule the dark blue zone represents observations within one standard deviation σ to either side of the mean μ which accounts for about 68 3 of the population two standard deviations from the mean dark and medium blue account for about 95 4 and three standard deviations dark medium and light blue for about 99 7 the methods given in the calculation methods section below are approximations for use in small sample statistics in general terms for very large populations following a normal distribution percentiles may often be represented by reference to a normal curve plot the normal distribution is plotted along an axis scaled to standard deviations or sigma σ displaystyle sigma units mathematically the normal distribution extends to negative infinity on the left and positive infinity on the right note however that only a very small proportion of individuals in a population will fall outside the 3 σ to 3 σ range for example with human heights very few people are above the 3 σ height level percentiles represent the area under the normal curve increasing from left to right each standard deviation represents a fixed percentile thus rounding to two decimal places 3 σ is the 0 13th percentile 2 σ the 2 28th percentile 1 σ the 15 87th percentile 0 σ the 50th percentile both the mean and median of the distribution 1 σ the 84 13th percentile 2 σ the 97 72nd percentile and 3 σ the 99 87th percentile this is related to the 68 95 99 7 rule or the three sigma rule note that in theory the 0th percentile falls at negative infinity and the 100th percentile at positive infinity although in many practical applications such as test results natural lower and or upper limits are enforced applications edit when internet service providers bill burstable internet bandwidth the 95th or 98th percentile usually cuts off the top 5 or 2 of bandwidth peaks in each month and then bills at the nearest rate in this way infrequent peaks are ignored and the customer is charged in a fairer way the reason this statistic is so useful in measuring data throughput is that it gives a very accurate picture of the cost of the bandwidth the 95th percentile says that 95 of the time the usage is below this amount so the remaining 5 of the time the usage is above that amount physicians will often use infant and children s weight and height to assess their growth in comparison to national median and other percentiles which are found in growth charts the 85th percentile speed of traffic on a road is often used as a guideline in setting speed limits and assessing whether such a limit is too high or low 7 8 in finance value at risk is a standard measure to assess in a model dependent way the quantity under which the value of the portfolio is not expected to sink within a given period of time and given a confidence value calculation methods edit this section possibly contains original synthesis source material should verifiably mention and relate to the main topic relevant discussion may be found on the talk page february 2023 learn how and when to remove this message interpolated and nearest rank exclusive and inclusive percentiles for 10 score distribution interpolated and nearest rank exclusive and inclusive percentiles for 10 score distribution there are many formulas or algorithms 9 for a percentile score hyndman and fan 3 identified nine and most statistical and spreadsheet software use one of the methods they describe 10 algorithms either return the value of a score that exists in the set of scores nearest rank methods or interpolate between existing scores and are either exclusive or inclusive nearest rank methods exclusive inclusive pc percentile specified 0 10 0 25 0 50 0 75 0 90 n number of scores 10 10 10 10 10 or ordinal rank pc n 1 2 5 5 7 5 9 rank or or 2 1 3 3 6 5 8 8 10 9 score at rank exc inc 2 1 3 3 4 3 5 5 7 5 the figure shows a 10 score distribution illustrates the percentile scores that result from these different algorithms and serves as an introduction to the examples given subsequently the simplest are nearest rank methods that return a score from the distribution although compared to interpolation methods results can be a bit crude the nearest rank methods table shows the computational steps for exclusive and inclusive methods interpolated methods exclusive inclusive pc percentile specified 0 10 0 25 0 50 0 75 0 90 n number of scores 10 10 10 10 10 or pc n 1 pc n 1 1 1 1 1 9 2 75 3 25 5 5 5 5 8 25 7 75 9 9 9 1 lorank or truncated 1 1 2 3 5 5 8 7 9 9 hirank or rounded up 2 2 3 4 6 6 9 8 10 10 loscore score at lorank 1 1 2 3 3 3 5 4 5 5 hiscore score at hirank 2 2 3 3 4 4 5 5 7 7 difference hiscore loscore 1 1 1 0 1 1 0 1 2 2 mod fractional part of or 0 1 0 9 0 75 0 25 0 5 0 5 0 25 0 75 0 9 0 1 interpolated score exc inc loscore mod difference 1 1 1 9 2 75 3 3 5 3 5 5 4 75 6 8 5 2 interpolation methods as the name implies can return a score that is between scores in the distribution algorithms used by statistical programs typically use interpolation methods for example the percentile exc and percentile inc functions in microsoft excel the interpolated methods table shows the computational steps the nearest rank method edit the percentile values for the ordered list 15 20 35 40 50 one definition of percentile often given in texts is that the p th percentile 0 p 100 displaystyle 0 p leq 100 of a list of n ordered values sorted from least to greatest is the smallest value in the list such that at least p percent of the data is less than or equal to that value this is calculated by first calculating the ordinal rank and then taking the value from the ordered list that corresponds to that rank the ordinal rank n is calculated using the formula n p 100 n displaystyle n left lceil frac p 100 times n right rceil using the nearest rank method on lists with fewer than 100 distinct values can result in the same value being used for more than one percentile a percentile calculated using the nearest rank method will always be a member of the original ordered list the 100th percentile is defined to be the largest value in the ordered list this method is also called the empirical distribution function method 11 the 50th percentile calculated using this method is equal to the usual value of the median if n is odd but not if n is even 11 the cdf method edit the cdf method was described e g by langford 11 given the order statistics v i i 1 2 n v i 1 v i i 1 2 n 1 displaystyle v_ i i 1 2 ldots n v_ i 1 geq v_ i forall i 1 2 ldots n 1 calculate x p 100 n displaystyle x frac p 100 times n the percentile is v x v 1 for x 0 v x for x 0 1 2 n 1 v x v x 1 2 for x 1 2 n 1 displaystyle v x begin cases v_ 1 text for x 0 v_ lceil x rceil text for x notin 0 1 2 ldots n 1 frac v_ x v_ x 1 2 text for x in 1 2 ldots n 1 end cases the 50th percentile calculated using this method is equal to the usual value of the median doubling the data leaves the calculated percentile value unchanged cdf percentile values for ordered list 15 20 35 40 50 n 5 displaystyle n 5 percentage p displaystyle p 0 p 20 displaystyle 0 leq p 20 p 20 displaystyle p 20 20 p 40 displaystyle 20 p 40 p 40 displaystyle p 40 40 p 60 displaystyle 40 p 60 p 60 displaystyle p 60 60 p 80 displaystyle 60 p 80 p 80 displaystyle p 80 80 p 100 displaystyle 80 p leq 100 x p 100 n displaystyle x frac p 100 times n 0 x 1 displaystyle 0 leq x 1 x 1 displaystyle x 1 1 x 2 displaystyle 1 x 2 x 2 displaystyle x 2 2 x 3 displaystyle 2 x 3 x 3 displaystyle x 3 3 x 4 displaystyle 3 x 4 x 4 displaystyle x 4 4 x 5 displaystyle 4 x leq 5 percentile 15 17 5 20 27 5 35 37 5 40 45 50 the linear interpolation between closest ranks method edit an alternative to rounding used in many applications is to use linear interpolation between adjacent ranks given the order statistics v i i 1 2 n v i 1 v i i 1 2 n 1 displaystyle v_ i i 1 2 ldots n v_ i 1 geq v_ i forall i 1 2 ldots n 1 the linear interpolation is simply accomplished by calculating v x v 1 for x 1 v n for x n v x x mod 1 v x 1 v x for 1 x n displaystyle v x begin cases v_ 1 text for x leq 1 v_ n text for x n v_ lfloor x rfloor x bmod 1 v_ lfloor x rfloor 1 v_ lfloor x rfloor text for 1 x n end cases where x displaystyle lfloor x rfloor uses the floor function to represent the integral part of x whereas x mod 1 displaystyle x bmod 1 uses the mod function to represent its fractional part the remainder after division by 1 this way v i v i for i 1 2 n displaystyle v i v_ i text for i 1 2 ldots n as we can see x is the continuous version of the subscript i linearly interpolating v between adjacent nodes there are two ways in which the variant approaches differ the first is in the linear relationship between the rank x the percent rank p 100 p displaystyle p 100p and a constant that is a function of the sample size n x f p n n c 1 p c 2 displaystyle x f p n n c_ 1 p c_ 2 there is the additional requirement that the midpoint of the range 1 n displaystyle 1 n corresponding to the median occur at p 0 5 displaystyle p 0 5 f 0 5 n n c 1 2 c 2 n 1 2 2 c 2 c 1 1 displaystyle begin aligned f 0 5 n frac n c_ 1 2 c_ 2 frac n 1 2 therefore 2c_ 2 c_ 1 1 end aligned and our revised function now has just one degree of freedom looking like this x f p n n 1 2 c p c displaystyle x f p n n 1 2c p c the second way in which the variants differ is in the definition of the function near the margins of the 0 1 displaystyle 0 1 range of p f p n displaystyle f p n should produce or be forced to produce a result in the range 1 n displaystyle 1 n which may mean the absence of a one to one correspondence in the wider region one author has suggested a choice of c 1 2 1 ξ displaystyle c tfrac 1 2 1 xi where ξ is the shape of the generalized extreme value distribution which is the extreme value limit of the sampled distribution first variant c 1 2 edit the result of using each of the three variants on the ordered list 15 20 35 40 50 sources matlab prctile function 12 11 x f p n p 1 2 p p 1 p n 1 p 0 p 1 n p p n 1 displaystyle x f p begin cases np frac 1 2 forall p in left p_ 1 p_ n right 1 forall p in left 0 p_ 1 right n forall p in left p_ n 1 right end cases where p i 1 n i 1 2 i 1 n n displaystyle p_ i frac 1 n left i frac 1 2 right i in 1 n cap mathbb n p 1 1 2 n p n 2 n 1 2 n displaystyle therefore p_ 1 frac 1 2n p_ n frac 2n 1 2n furthermore let p i 100 p i displaystyle p_ i 100p_ i the inverse relationship is restricted to a narrower region p 1 n x 1 2 x 1 n r displaystyle p frac 1 n left x frac 1 2 right x in 1 n cap mathbb r second variant c 1 edit source some software packages including numpy 13 and microsoft excel 5 up to and including version 2013 by means of the percentile inc function noted as an alternative by nist 10 x f p n p n 1 1 p 0 1 displaystyle x f p n p n 1 1 text p in 0 1 p x 1 n 1 x 1 n displaystyle therefore p frac x 1 n 1 text x in 1 n note that the x p displaystyle x leftrightarrow p relationship is one to one for p 0 1 displaystyle p in 0 1 the only one of the three variants with this property hence the inc suffix for inclusive on the excel function third variant c 0 edit the primary variant recommended by nist 10 adopted by microsoft excel since 2010 by means of percentil exc function however as the exc suffix indicates the excel version excludes both endpoints of the range of p i e p 0 1 displaystyle p in 0 1 whereas the inc version the second variant does not in fact any number smaller than 1 n 1 displaystyle frac 1 n 1 is also excluded and would cause an error x f p n 1 p 0 1 n 1 p n 1 p 1 n 1 n n 1 n p n n 1 1 displaystyle x f p n begin cases 1 text p in left 0 frac 1 n 1 right p n 1 text p in left frac 1 n 1 frac n n 1 right n text p in left frac n n 1 1 right end cases the inverse is restricted to a narrower region p x n 1 x 0 n displaystyle p frac x n 1 text x in 0 n the weighted percentile method edit see also weighted median in addition to the percentile function there is also a weighted percentile where the percentage in the total weight is counted instead of the total number there is no standard function for a weighted percentile one method extends the above approach in a natural way suppose we have positive weights w 1 w 2 w 3 w n displaystyle w_ 1 w_ 2 w_ 3 dots w_ n associated respectively with our n sorted sample values let s n k 1 n w k displaystyle s_ n sum _ k 1 n w_ k the sum of the weights then the formulas above are generalized by taking p n 1 s n s n w n 2 displaystyle p_ n frac 1 s_ n left s_ n frac w_ n 2 right when c 1 2 displaystyle c 1 2 or p n s n c w n s n 1 2 c w n displaystyle p_ n frac s_ n cw_ n s_ n 1 2c w_ n for general c displaystyle c and v v k p p k p k 1 p k v k 1 v k displaystyle v v_ k frac p p_ k p_ k 1 p_ k v_ k 1 v_ k the 50 weighted percentile is known as the weighted median see also edit mathematics portal decile percentile rank quantile sample maximum and minimum summary statistics notes edit the typical definition based on greater than may be called exclusive in contrast to the alternative definition involving greater than or equal to so called because it includes one additional data point references edit stephens larry j 2011 04 12 schaum s outline of statistics for engineers mcgraw hill professional isbn 978 0 07 173647 3 couallier vincent gerville réache léo huber carol catherine limnios nikolaos mesbah mounir 2013 12 31 statistical models and methods for reliability and survival analysis john wiley sons isbn 978 1 84821 619 8 1 2 hyndman rob j fan yanan november 1996 sample quantiles in statistical packages american statistician 50 4 american statistical association 361 365 doi 10 2307 2684934 jstor 2684934 lane david percentiles retrieved 2007 09 15 1 2 pottel hans statistical flaws in excel pdf archived from the original pdf on 2013 06 04 retrieved 2013 03 25 schoonjans f de bacquer d schmid p 2011 estimation of population percentiles epidemiology 22 5 750 751 doi 10 1097 ede 0b013e318225c1de pmc 3171208 pmid 21811118 johnson robert kuby patricia 2007 applied example 2 15 the 85th percentile speed limit going with 85 of the flow elementary statistics 10th ed cengage learning p 102 isbn 9781111802493 rational speed limits and the 85th percentile speed pdf lsp org louisiana state police archived from the original pdf on 23 september 2018 retrieved 28 october 2018 wessa p 2021 percentiles in free statistics software office for research development and education retrieved 13 november 2021 1 2 3 engineering statistics handbook percentile ...
|
