The quantile or probit function, as you can see from the link (see "Computatuon"), is computed with inverse gaussian error function which I hope is downloadable for calculators like TI-89. Look here for instance.

Answer from ttnphns on Stack Exchange
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Statology
statology.org › home › how to find quartiles using mean & standard deviation
How to Find Quartiles Using Mean & Standard Deviation
September 27, 2021 - You can use the following formulas to find the first (Q1) and third (Q3) quartiles of a normally distributed dataset: Q1 = μ - (.675)σ Q3 = μ + (.675)σ
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Stat Trek
stattrek.com › online-calculator › statistics
Statistics Calculator
Statistics calculator: Computes mean, median, mode, standard deviation, variance, range, interquartile range, upper quartile, lower quartile, and skewness.
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Standard Deviation Calculator
standarddeviationcalculator.io › quartile-calculator
Quartile Calculator
Click calculate. Reset for a different dataset. ... Feedback Submitted Successfully. Feedback Submitted Successfully. ... Find q1, q2, q3, and the interquartile range using the quartiles calculator. It is a statistical tool to assist in calculating the quartiles of any given dataset.
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Quora
quora.com › How-do-you-find-Q1-and-Q3-from-mean-and-standard-deviation
How to find Q1 and Q3 from mean and standard deviation - Quora
Answer (1 of 3): If you are willing to assume the data are normally distributed or approximately so, then the inter-quartile range (IQR), which is defined as Q3 − Q1, is equal to SD × 1.35 and mean = median.
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Inch Calculator
inchcalculator.com › home › math › statistics › statistics calculator
Statistics Calculator - Inch Calculator
December 5, 2023 - Use our statistics calculator to find the mean, median, mode, range, standard deviation, variance, quartiles, and midrange for a data set.
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StatsKingdom
statskingdom.com › descriptive-statistics-calculator.html
Descriptive statistics calculator - Numerical/Categorical data
Comprehensive descriptive statistics calculator. Optional Excel input. Computes statistics like minimum, mean, standard deviation, quartiles, IQR, observations, and skewness. Handles both numerical and categorical data.
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Calculator Online
calculator-online.net › quartile-calculator
Quartile Calculator - You can find your data quotients.
This Quartile calculator calculates the quartiles (Q1, Q2, and Q3) of the given data set, along with key statistics and a visual representation to increase understanding of the data distribution. In addition to that, it also provides: ... Quartiles are the statistical values that divide the dataset into four equal parts. Three quartiles (Q1, Q2, and Q3) create a four interval. Each of them contains roughly 25% of the data points. ... The lower quartile (Q1) shows the 25th percentile of the data set. This means that 75% of the data points fall above it.
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AtoZmath
atozmath.com › StatsG.aspx
Quartile calculator for grouped data
Find Quartile calculator for grouped data - Find Quartile for grouped data, step-by-step online
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Calculator.iO
calculator.io › statistics calculators › quartile calculator
Quartile Calculator
This statistics calculator will calculate the first quartile (Q1), second quartile (Q2) or the median, third quartile (Q3), minimum value, and maximum value of the given data set. Further, it calculates the interquartile range and the range too. You just need to type or copy and paste the data and click the “calculate” button. Make sure to separate each number with a comma or a space.
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Springer
link.springer.com › home › bmc medical research methodology › article
Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range | BMC Medical Research Methodology
December 19, 2014 - Further discussion on the choice of α can be seen, for example, in [8] and [9]. Finally, by (7) and (8) with r = n and α = 0.375, we estimate the sample standard deviation by ... In the statistical software R, the upper zth percentile Φ -1(z) can be computed by the command “qnorm(z)”. ... 2 assumes that the first quartile, q 1, and the third quartile, q 3, are also available in addition to
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Calculator.net
calculator.net › home › math › standard deviation calculator
Standard Deviation Calculator
This free standard deviation calculator computes the standard deviation, variance, mean, sum, and error margin of a given data set.
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CalculatorSoup
calculatorsoup.com › calculators › statistics › descriptivestatistics.php
Descriptive Statistics Calculator
November 4, 2025 - Calculator online for descriptive or summary statistics including minimum, maximum, range, sum, size, mean, median, mode, standard deviation, variance, midrange, quartiles, interquartile range, outliers, sum of squares, mean deviation, absolute deviation, root mean square, standard error of the mean, skewness, kurtosis, kurtosis excess in Excel, coefficient of variation and frequency.
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Online Stat Book
onlinestatbook.com › 2 › calculators › normal_dist.html
Normal Distribution
Online Statistics Education: An Interactive Multimedia Course of Study · Developed by Rice University (Lead Developer), University of Houston Clear Lake, and Tufts University
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CalculatorSoup
calculatorsoup.com › calculators › statistics › quartile-calculator.php
Quartile Calculator | Interquartile Range Calculator
November 4, 2025 - Calculate first, second and third quartiles, Q1 Q2 Q3, for a set of data. Find median, interquartile range IQR, dataset minimum and maximum for statistics data analysis.
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Scribbr
scribbr.com › home › quartiles & quantiles | calculation, definition & interpretation
Quartiles & Quantiles | Calculation, Definition & Interpretation
June 21, 2023 - Calculate n * (2 / 4). If n * (2 / 4) is an integer, the second quartile is the mean of the numbers at positions n * (2 / 4) and n * (2 / 4) + 1.
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HackMath
hackmath.net › en › calculator › quartile-q1-q3
Quartile calculator Q1, Q3 (statistics)
The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell. 75th percentile (quartille Q3) Find 75th percentile for 30,42,42,46,46,46,50,50,54 · 45 percentile Given the following data 11 15 24 33 10 35 23 25 40 What is P45? Find mean Find the mean of two numbers: -4 and 5 (the first is negative four).
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Numiqo
numiqo.com
Statistics Calculator [t-Test, Chi-square, Regression, Correlation,...]
Descriptive statisticsLocation parameterMeanMedianModeDispersion parameterStandard DeviationVarianceRangeQuartilesSkew and KurtosisTests for normal distribution (normality)Kolmogorov-Smirnov, Shapiro-Wilk and Anderson-Darling TestConfidence interval for meanFrequency tableContingency tableCharts (Diagrams, Plots)Bar ChartBoxplotViolin PlotRaincloud PlotHistogramScatter PlotLine ChartSankey DiagramBland-Altman PlotPareto ChartQuantile-Quantile PlotHypothesis Testingp-ValueOne sample t-testt-Test for independent samplest-test for paired samplesBinomial testChi-square testANOVAOne Way ANOVATwo Wa