Series MI-07 · 195 instruments catalogued
Statistics
Paste your data; get the distribution drawn properly.
In Service
179 built and verified5 Number Summary Calculator
Get the minimum, Q1, median, Q3 and maximum in one pass — the exact five numbers needed to draw a box plot, with the working shown.
In service MI-07-0066 Sided Dice Probability Calculator
Find the probability of rolling at least one favorable face in several rolls of a six-sided die — the calculation behind the historic de Méré dice problem.
In service MI-07-00890% Confidence Interval Calculator
Compute a 90% confidence interval from a sample mean, standard deviation and sample size — the narrowest standard CI level, built for quick screening.
In service MI-07-00995% Confidence Interval Calculator
Compute a 95% confidence interval from a sample mean, standard deviation and sample size — the field-standard critical value (z = 1.96) most research uses.
In service MI-07-01099% Confidence Interval Calculator
Compute a 99% confidence interval from a sample mean, standard deviation and sample size — the widest standard CI level, built for high-stakes claims.
In service MI-07-011AB Test Calculator
Turn visitor and conversion counts from two variants into a two-proportion z-statistic — see the conversion rates and how far apart they really are.
In service MI-07-012Absolute Uncertainty Calculator
Enter repeated measurements of the same quantity and get a best estimate plus its absolute uncertainty, using the half-range (max minus min, over two) method.
In service MI-07-013Accuracy Calculator
Calculate classification accuracy from a confusion matrix: enter true/false positives and negatives to see what share of all predictions were correct.
In service MI-07-014AND Probability Calculator
Multiply two independent probabilities to find P(A and B) — the chance both events happen — with the working shown step by step.
In service MI-07-015ANOVA Calculator
Compare three groups' means at once with one-way ANOVA — enter each group's raw data and get the sum-of-squares breakdown and the F-statistic in one pass.
In service MI-07-016Ascending Order Calculator
Paste any list of numbers and get them arranged smallest to largest instantly — negatives, decimals and duplicates all sort correctly.
In service MI-07-017Average Rating Calculator
Enter how many 1- through 5-star ratings a product or app received, and calculate the true weighted-average star rating from the full breakdown.
In service MI-07-018Bayes' Theorem Calculator
Enter a prior, a likelihood and the evidence probability to find the posterior P(A|B) — how new evidence should actually change what you believe.
In service MI-07-019Benford's Law Calculator
Find the probability that a naturally occurring number starts with a given digit under Benford's law — the statistical basis for spotting fabricated data.
In service MI-07-020Bertrand's Box Paradox
Given gold-gold and gold-silver boxes, find the probability the hidden second coin is gold after the first is gold — the classic 2/3 result, generalized.
In service MI-07-021Bertrand's Paradox
Pick a method for choosing a random chord and get the probability it's longer than the triangle's side — three classic methods, three different answers.
In service MI-07-022Beta Distribution Calculator
Enter the two shape parameters alpha and beta and get the Beta distribution's mean, variance, and standard deviation — the moments that summarize its shape.
In service MI-07-023Binomial Distribution Calculator
Calculate P(X = k), the exact probability of getting k successes in n trials at a fixed success probability p — the binomial probability mass function.
In service MI-07-024Birthday Paradox Calculator
Enter a group size and find the probability at least two people share a birthday — the famous result that only 23 people are needed to pass 50%.
In service MI-07-025Bonferroni Correction Calculator
Divide your significance level by the number of comparisons to get a Bonferroni-adjusted alpha — the standard guard against false positives across many tests.
In service MI-07-026Box Plot Calculator
Enter a data set and get every number needed to draw a box-and-whisker plot: min, quartiles, median, max, IQR, and the 1.5×IQR outlier fences.
In service MI-07-027Boy or Girl Paradox
See why 'at least one child is a boy' gives P(both boys) = 1/3, while 'a specific child is a boy' gives 1/2 — the exact wording changes the sample space.
In service MI-07-028Central Limit Theorem Calculator
Apply the Central Limit Theorem to find a sample mean's expected value and standard error, E[x̄] = μ and SE(x̄) = σ/√n, from population μ, σ, and sample size n.
In service MI-07-029Chebyshev's Theorem Calculator
Find the guaranteed minimum percentage of data within k standard deviations of the mean — valid for any distribution, not just bell-shaped ones.
In service MI-07-030Chi-Square Calculator
Enter up to four observed and expected category counts to get the chi-square statistic — one number measuring how far your data strays from what you expected.
In service MI-07-031Class Width Calculator
Enter your data's range and how many classes you want to get the class width for a frequency table or histogram: (max − min) ÷ classes.
In service MI-07-032Coefficient of Determination Calculator (R-squared)
Enter actual and predicted values and get R², the coefficient of determination, showing how much of the variation in the actual data your predictions explain.
In service MI-07-033Coefficient of Variation Calculator
Calculate the coefficient of variation, CV = (s / mean) × 100% — spread relative to the average, so you can compare risk or variability across different scales.
In service MI-07-034Cohen's D Calculator
Compute Cohen's d from two sample means, deviations and sizes — a standardized effect size showing how big a difference is, not just whether it's significant.
In service MI-07-035Coin Flip Probability Calculator
Enter the number of flips and the number of heads you want, and get the exact probability of landing on precisely that many heads in a fair coin's flips.
In service MI-07-037Coin Toss Streak Calculator
Find the probability that n coin flips contain a run of consecutive heads at least k long — streaks happen more often than intuition suggests.
In service MI-07-038Combination Calculator
Find nCr, the number of ways to choose r items from a set of n when order doesn't matter — raffle winners, lottery picks, team selections.
In service MI-07-039Combination without Repetition Calculator
Count unordered selections where each item can be chosen at most once — nCr = n! / (r!(n − r)!) — with a direct contrast against repetition allowed.
In service MI-07-040Combinations with Repetition Calculator
Count unordered selections where the same item can be chosen more than once — C(n + r − 1, r), the stars-and-bars formula for combinations with repeats.
In service MI-07-041Conditional Probability Calculator
Divide P(A and B) by P(B) to find P(A|B) — the chance A happens given that B already has — with the arithmetic shown in full.
In service MI-07-042Confidence Interval Calculator
Build a confidence interval at any of five levels — 80%, 90%, 95%, 98% or 99% — from a sample mean, standard deviation and sample size, all in one instrument.
In service MI-07-043Confusion Matrix Calculator
Enter true/false positive and negative counts from a classifier and get accuracy, precision, recall, specificity, and F1 — all five metrics from one 2x2 table.
In service MI-07-044Constant of Proportionality Calculator
Enter an x and y pair from a direct-proportion relationship to find k, the constant of proportionality, where y = kx.
In service MI-07-045Continuity Correction Calculator
Find the x - 0.5 and x + 0.5 correction values used when approximating a discrete distribution, like the binomial, with the continuous normal curve.
In service MI-07-046Correlation Coefficient Calculator
Enter paired x and y values and get Pearson's correlation coefficient r and r-squared, measuring how closely the two variables move together in a straight line.
In service MI-07-047Correlation Coefficient Calculator (Matthews)
Calculate Matthews correlation coefficient from a confusion matrix: enter TP, FP, TN, FN for a single -1 to +1 score robust to class imbalance.
In service MI-07-048Covariance Calculator
Enter paired x and y values and get both sample and population covariance, the raw measure of whether two variables tend to rise and fall together.
In service MI-07-049Critical Value Calculator
Enter any significance level alpha and get the matching one-tailed and two-tailed critical z-values, computed from the standard normal distribution.
In service MI-07-050Cubic Regression Calculator
Enter at least 4 paired x, y points and get the best-fit cubic curve y = ax³+bx²+cx+d, its four coefficients, and R-squared for how well it fits.
In service MI-07-054Decile Calculator
Enter a data set and a decile from 1 to 9, and get the value at that decile — the same linear-interpolation method used by this site's percentile calculator.
In service MI-07-055Decimal Odds Calculator
Convert an implied probability into decimal odds, the European-style payout multiplier: stake x decimal odds = total return, including your original stake.
In service MI-07-057Degrees of Freedom Calculator
Enter your sample size to get degrees of freedom for a one-sample t-test or variance estimate — the n − 1 figure you'll need for a t-table lookup.
In service MI-07-001Descriptive Statistics Calculator
Paste a data set; get mean, median, quartiles, spread and range — with the working shown.
In service MI-07-058Dice Average Calculator
Find the long-run average result of rolling a fair die with any number of sides — the expected value, (sides + 1) / 2, for d4, d6, d20, d100, or any custom die.
In service MI-07-059Dice Probability Calculator
Enter any number of dice, any number of sides, and a target sum, and get the exact probability of rolling that sum — general n-dice sum probability.
In service MI-07-061Dispersion Calculator
Enter a data set and get five dispersion measures at once: range, sample variance, sample standard deviation, coefficient of variation, and interquartile range.
In service MI-07-063Dot Plot Calculator
Enter a data set and get an exact tally of every distinct value's frequency — the value-by-value counts a dot plot displays as stacked dots, unbinned.
In service MI-07-064Effect Size Calculator
Enter a reported t-statistic and both sample sizes and convert it directly into Cohen's d, the standardized effect size — no raw means or deviations needed.
In service MI-07-065Empirical Rule Calculator
Look up the standard 68%, 95% or 99.7% figure for how much normally distributed data falls within 1, 2 or 3 standard deviations of the mean.
In service MI-07-066Error Propagation Calculator
Enter two measured values and their uncertainties, and get the propagated uncertainty for their sum/difference, product, and quotient, all at once.
In service MI-07-067Expected Value Calculator
Calculate the expected value (EV) of an uncertain outcome by multiplying each possible result by its probability and adding the results together.
In service MI-07-068Exponential Distribution Calculator
Find the exponential distribution's density f(x) and cumulative probability F(x) for a given rate λ — the model for waiting times between random events.
In service MI-07-069Exponential Growth Prediction Calculator
Enter a starting amount, a growth rate per period, and a number of periods, and predict the resulting amount using the discrete compounding growth model.
In service MI-07-070Exponential Regression Calculator
Fit an exponential curve y = a·e^(b·x) through paired x/y data by log-linearizing and running least squares, then read off the growth or decay rate.
In service MI-07-071F-statistic calculator
Divide one sample variance by another to get the F-statistic — the building block of the F-test for comparing variability between two groups.
In service MI-07-072False Positive Calculator
Given a test's known false-positive rate and how many truly negative cases you're testing, calculate the expected number of false alarms it will produce.
In service MI-07-073False Positive Paradox Calculator
See the false positive paradox: enter sensitivity, specificity and disease prevalence to find positive predictive value for a positive test result.
In service MI-07-074First Quartile Calculator
Find Q1, the value below which the bottom quarter of your data falls — a single cut point, computed by linear interpolation and shown with the working.
In service MI-07-075Fisher's Exact Test Calculator
Enter the four cell counts of a 2×2 table and get the exact hypergeometric probability of that specific table, given its row and column totals.
In service MI-07-076Fractional Odds Calculator
Convert fractional odds like 5/2 into decimal odds. Enter the numerator and denominator from a UK-style odds quote and get the equivalent payout multiplier.
In service MI-07-077Frequency Distribution Calculator
Group raw numeric data into equal-width classes and get a full frequency table showing each class interval and how many values fall inside it.
In service MI-07-078Frequency Polygon Calculator
Group raw data into equal-width classes and get each class's midpoint paired with its count, ready to plot as a frequency polygon's connected line.
In service MI-07-079Geometric Distribution Calculator
Find P(X = k) and P(X ≤ k) for the geometric distribution — the probability that the first success in repeated trials lands exactly on, or by, trial k.
In service MI-07-080Greatest To Least Calculator
Paste any list of numbers and get them ranked largest to smallest instantly — the leaderboard order for scores, sales figures or race times.
In service MI-07-081Grouped Data Standard Deviation Calculator
Enter class midpoints and their frequencies to estimate the mean, sample standard deviation, and population standard deviation of grouped data.
In service MI-07-082Histogram Calculator
Group raw numeric data into equal-width classes and get each bar's height (count) — everything you need to sketch a histogram by hand.
In service MI-07-083Hypergeometric Distribution Calculator
Find P(X = k), the probability of exactly k successes drawing a fixed sample without replacement from a finite population — the aces-in-a-hand kind of problem.
In service MI-07-084Hypothesis Testing Calculator
Run a one-sample z-test from your sample mean, hypothesized mean, standard deviation, and sample size, and get an explicit reject/fail-to-reject decision.
In service MI-07-085Implied Probability Calculator
Convert decimal odds into the implied probability behind them. Enter a decimal odds figure and get the percentage chance the market is pricing in.
In service MI-07-086Index of Qualitative Variation Calculator
Enter the frequency counts across 5 categories and calculate the Index of Qualitative Variation — a 0-to-1 measure of diversity for nominal, categorical data.
In service MI-07-087Inverse Normal Distribution Calculator
Enter a cumulative probability p and get the standard normal z-value where Φ(z) = p — the inverse standard normal CDF, computed to near machine precision.
In service MI-07-088IQR Calculator — Interquartile Range
Calculate the interquartile range: the spread of the middle 50% of your data, Q3 minus Q1 — a measure of scale that resists outliers unlike the range.
In service MI-07-089Joint Probability Calculator
Find the joint probability that two independent events both happen, P(A and B), by multiplying their individual probabilities together.
In service MI-07-090Least to Greatest Calculator
Paste any list of numbers and arrange them from least to greatest instantly — negatives, decimals, and duplicates all sort correctly, in any starting order.
In service MI-07-091Least to Greatest Decimals Calculator
Sort a list of decimal numbers from least to greatest correctly — avoids the classic trap where a number with more digits looks bigger but actually isn't.
In service MI-07-092Linear Regression Calculator
Fit the best-fit straight line through paired x/y data using ordinary least squares, and get the slope, intercept, correlation, and R-squared in one pass.
In service MI-07-093Lognormal Distribution Calculator
Enter mu, sigma, and x to calculate the lognormal probability density, mean, variance, median, and mode — for data that's normal on a log scale.
In service MI-07-094Lottery Calculator
Enter the pool size, how many numbers are picked, and any bonus pool to calculate exact lottery odds using combinatorics — the same math real lotteries use.
In service MI-07-095Lower Fence Calculator
Calculate the lower fence, Q1 − 1.5 × IQR — the boundary below which a value counts as an unusually low outlier, using the standard box-plot rule.
In service MI-07-096Mann-Whitney U Test Calculator
Calculate the Mann-Whitney U statistic (U1, U2, and z-approximation) from two independent samples — a nonparametric test for whether one group scores higher.
In service MI-07-097Margin of Error Calculator
Calculate the margin of error for a confidence interval — how far a sample mean could plausibly sit from the true population mean, given s, n and z.
In service MI-07-098McNemar's Test Calculator
Enter the discordant-pair counts B and C from a before/after table to calculate McNemar's chi-square statistic, plus the continuity-corrected version.
In service MI-07-099Mean Absolute Deviation Calculator
Calculate the mean absolute deviation — the average distance every value sits from the mean — a simpler alternative to variance and standard deviation.
In service MI-07-100Mean Median Mode Calculator
Enter a data set and get the mean, median, and mode together in one pass — the three classic measures of central tendency, calculated and compared side by side.
In service MI-07-101Median Absolute Deviation Calculator
Calculate the median absolute deviation — the median distance every value sits from the data's median — a spread measure that resists outliers well.
In service MI-07-102Median Calculator
Find the median of any data set: sort your numbers and read the true middle value, a measure of centre that a single outlier can't drag around.
In service MI-07-103Midrange Calculator
Calculate the midrange of a data set — the midpoint between the highest and lowest value, the fastest possible estimate of centre when you only have a moment.
In service MI-07-104Minimum and Maximum Calculator
Find the smallest and largest values in any list at once — no interpolation, no rounding, just the two extremes and a quick spread check.
In service MI-07-105Mode Calculator
Find the mode of a data set — the most frequently occurring value — along with its exact frequency count and a flag for whether the data is multimodal.
In service MI-07-106Moneyline Odds Calculator
Convert American moneyline odds like +150 or -200 into decimal odds. Enter the plus or minus figure from a US sportsbook and get the payout multiplier.
In service MI-07-107Monty Hall Problem Calculator
See why switching doors doubles your odds in the classic 3-door Monty Hall problem — and how the advantage changes as the number of doors grows.
In service MI-07-108MSE Calculator — Mean Squared Error
Enter paired actual and predicted values to get MSE and RMSE — the standard measures of how far a model's predictions land from reality, on average.
In service MI-07-109Negative Binomial Distribution Calculator
Find P(X = k), the probability of exactly k failures occurring before the rth success in a series of independent trials at success probability p.
In service MI-07-110Normal Approximation Calculator
Enter n, p and a target value to approximate a binomial probability using the normal distribution, with the standard continuity correction applied.
In service MI-07-111Normal Distribution Calculator
Enter a value, mean and standard deviation to get the z-score, probability density, and cumulative probability P(X ≤ x) under a normal distribution.
In service MI-07-112Normal Probability Calculator for Sampling Distributions
Enter a population mean, standard deviation and sample size to find the probability a sample mean falls at or below a target value, via the CLT.
In service MI-07-113Odds Calculator
Convert a probability into odds in favor, expressed as X to 1. Enter a percentage chance and read the equivalent betting-style odds instantly.
In service MI-07-114OR Probability Calculator
Add two probabilities and subtract their overlap to find P(A or B) — the chance at least one event happens — worked step by step.
In service MI-07-115Order from Least to Greatest Calculator
Paste any list of numbers — positive, negative, or decimal — and get them instantly rearranged from least to greatest, sorted order shown clearly.
In service MI-07-116Ordering Decimals Calculator
Paste a list of decimal numbers and get them correctly ordered from smallest to largest — avoids the common trap of comparing decimals digit by digit.
In service MI-07-117Ordering Numbers Calculator
Paste a list of whole numbers, negatives, or decimals and instantly see them arranged in ascending order, from smallest to largest.
In service MI-07-118Outlier Calculator
Enter a data set and one test value; get a straight yes/no on whether that point is a statistical outlier by the 1.5×IQR fence rule, with both fences shown.
In service MI-07-119P-Hat Calculator
Calculate the sample proportion, p-hat = x / n — the fraction of successes observed in a sample, the building block behind polls and proportion tests.
In service MI-07-120p-value Calculator
Enter a z-test statistic to get the left-tailed, right-tailed and two-tailed p-values — the standard figures used to judge significance in a z-test.
In service MI-07-121Parrondo's Paradox Calculator
Enter win probabilities for two losing games — a fixed game A and a capital-dependent game B — to see expected profits alone and combined, the classic paradox.
In service MI-07-122Password Combination Calculator
Calculate how many possible passwords a character set and length produce — the full brute-force search space an attacker guessing blindly would have to cover.
In service MI-07-123Pearson Correlation Calculator
Enter paired x and y values to get Pearson's r and r² — the standard measure of how strong, and in which direction, a linear relationship runs.
In service MI-07-124Percentile Calculator
Pick any percentile from 0 to 100 and get the matching value from your data set — computed by linear interpolation, with the working shown.
In service MI-07-125Percentile Rank Calculator
Enter a dataset and a value to find its percentile rank — the percentage of values in the set that fall at or below it.
In service MI-07-126Permutation Calculator
Find nPr, the number of ways to arrange r items from a set of n when order matters — medal placings, seating orders, race finishes.
In service MI-07-127Permutation with Repetition Calculator
Count ordered arrangements where each position reuses the full set of options — n^r — for PIN codes, binary strings, and repeatable symbol sequences.
In service MI-07-128Permutation without Repetition Calculator
Count ordered arrangements where each item can be used only once — nPr = n! / (n − r)! — with a direct contrast against arranging with repeats allowed.
In service MI-07-129Pie Chart Angle Calculator
Enter a slice's value and the total to get its angle in degrees out of 360 — the exact angle to mark with a protractor or set in chart code.
In service MI-07-130Pie Chart Calculator
Enter a slice's value and the total to get both its percentage share and its angle in degrees — everything needed to size a pie-chart slice.
In service MI-07-131Pie Chart Percentage Calculator
Enter a slice's value and the total to get its percentage share of the whole — the number needed for a pie-chart data table or legend.
In service MI-07-132Point Estimate Calculator
Enter successes and sample size to get four point-estimate methods for a population proportion, plus a recommended estimate based on your data.
In service MI-07-133Poisson Distribution Calculator
Calculate P(X = k), the probability of exactly k events occurring in a fixed interval, given an average event rate λ — from call volumes to typos per page.
In service MI-07-134Polynomial Regression Calculator
Fit a polynomial curve of degree 1 through 5 to paired x, y data by least squares — get every coefficient plus R² goodness of fit.
In service MI-07-135Pooled Standard Deviation Calculator
Combine two samples' standard deviations and sizes into a single pooled standard deviation — the shared-spread estimate used in Cohen's d and the t-test.
In service MI-07-136Population Variance Calculator
Calculate population variance (σ²) when your data already covers every member of the group you care about — no sampling correction needed.
In service MI-07-137Possible Combinations Calculator
Multiply independent choice counts together to find the total number of possible outcomes — license plates, meal combos, and outfit builds.
In service MI-07-138Post-Test Probability Calculator
Calculate post-test probability from pre-test probability, sensitivity and specificity, using the odds-and-likelihood-ratio Bayesian update method.
In service MI-07-139Power Analysis Calculator
Enter an effect size, standard deviation, sample size and significance level to estimate statistical power — the odds your test correctly detects a real effect.
In service MI-07-140Probability Calculator
Enter favorable and total outcomes to find the probability of an event as a percentage — the classical odds-in-your-favor calculation, worked step by step.
In service MI-07-141Probability Fraction Calculator
Enter favorable and total outcomes to get the probability as an exact reduced fraction, like 1/13, using the same GCD method that simplifies any fraction.
In service MI-07-142Probability of 3 Events Calculator
Multiply three independent events' probabilities together to find P(A and B and C) — the chance that all three happen at the same time.
In service MI-07-143Process Capability Index Calculator
Enter spec limits, process mean and standard deviation to get Cp and Cpk — the two core measures of whether a process actually fits inside its tolerance.
In service MI-07-144Quadratic Regression Calculator
Enter paired x, y data to fit a quadratic curve by least squares and get the a, b, c coefficients along with R² goodness of fit.
In service MI-07-145Quartic Regression Calculator
Fit a degree-4 (quartic) polynomial to x,y data using least squares, returning all five coefficients and R² — for curves a line or parabola can't capture.
In service MI-07-146Quartile Calculator
Enter a data set and get all three quartiles — Q1, the median and Q3 — at once, split by linear interpolation and shown with the working.
In service MI-07-152Range Calculator
Find the range of any data set instantly: the highest value minus the lowest — the simplest measure of how spread out your numbers are.
In service MI-07-153Raw Score Calculator
Enter a target z-score, a mean and a standard deviation to find the raw value it corresponds to — the reverse of standardizing a score.
In service MI-07-154Rayleigh Distribution Calculator
Find the Rayleigh distribution's density f(x), cumulative probability F(x) and mean for scale σ — the model for wind speed, wave height and signal magnitude.
In service MI-07-155Relative Error Calculator
Find the relative error between a measured value and its true or accepted value, expressed as a percentage — a fast way to judge how good a measurement is.
In service MI-07-156Relative Frequency Calculator
Convert a raw count into relative frequency — the share of the total that outcome represents, shown as a percentage, from a frequency and a total count.
In service MI-07-157Relative Risk Calculator
Calculate relative risk from a 2×2 exposure/outcome table: enter exposed and unexposed group counts to compare event risk between the two groups directly.
In service MI-07-158Relative Standard Deviation Calculator
Calculate %RSD = (s / mean) × 100% — the lab precision figure chemists and QC analysts use to judge whether repeat instrument readings are tight enough.
In service MI-07-159Residual Calculator
Calculate a residual — the gap between an observed value and a model's predicted value — the basic building block behind every regression diagnostic.
In service MI-07-160Risk Calculator
Compare two options by expected risk — probability of loss times amount at stake — to see which choice carries less risk, not just the bigger downside.
In service MI-07-161Roulette Payout Calculator
Pick a bet type and wheel type to see the payout ratio and the exact house edge — 2.70% on a European wheel, 5.26% on an American wheel, for standard bets.
In service MI-07-162RSE Calculator — Relative Standard Error
Calculate the standard error and relative standard error (%RSE) of a sample mean from its standard deviation and sample size — a measure of estimate precision.
In service MI-07-163Sample Size Calculator
Find the minimum sample size needed to hit a target margin of error at your chosen confidence level: n = ceil((z x s / E)^2), rounded up to the next whole n.
In service MI-07-164Sampling Distribution of the Sample Proportion Calculator
Find E[p̂] and SE(p̂), the expected value and standard error of a sample proportion — how much a poll or survey percentage would wobble on repeat sampling.
In service MI-07-165Sampling Error Calculator
Calculate the standard error of a sample proportion, SE = sqrt(p-hat(1-p-hat)/n) — how much p-hat would wobble if you resampled from the same population.
In service MI-07-166Sensitivity and Specificity Calculator
Calculate sensitivity (true positive rate) and specificity (true negative rate) from true/false positive/negative counts — the two core test-accuracy measures.
In service MI-07-167Sensitivity Calculator
Calculate sensitivity (true positive rate) from a confusion matrix: enter true positives and false negatives to see what share of real positives get caught.
In service MI-07-168Shannon Entropy Calculator
Calculate Shannon entropy in bits from probabilities — the information-theory measure of how unpredictable a distribution is, in Shannon's base-2 units.
In service MI-07-169Simpson’s Diversity Index Calculator
Calculate Simpson's index, Diversity Index, and Reciprocal Index from species (or category) proportions — the standard ecology measures of community diversity.
In service MI-07-170Skewness Calculator
Calculate skewness (the Fisher-Pearson coefficient g1) from a dataset — whether a distribution's tail leans longer left or right of its center.
In service MI-07-171SMp(x) Distribution Calculator
Evaluate SMp(x), a piecewise double-power peaked density shaped by a lower limit, peak location, upper limit, and independent left/right steepness powers.
In service MI-07-172Spearman's Correlation Calculator
Calculate Spearman's rank correlation coefficient (rho) between paired variables — how consistently they move together, based on ranks rather than raw values.
In service MI-07-173Specificity Calculator
Calculate specificity (true negative rate) from a confusion matrix: enter true negatives and false positives to see what share of real negatives get cleared.
In service MI-07-174Standard Deviation Calculator
Calculate standard deviation from any data set — both the sample (s) and population (σ) forms, computed side by side so you can compare them directly.
In service MI-07-175Standard Deviation Index Calculator
Calculate the Standard Deviation Index (SDI) for a lab QC result, comparing your lab's mean against a peer group's mean in standard-deviation units.
In service MI-07-176Standard Deviation of Sample Mean Calculator
Estimate the standard deviation of the sampling distribution of the mean — the Central Limit Theorem quantity behind confidence intervals, s divided by √n.
In service MI-07-177Standard Error Calculator
Calculate the standard error of the mean (SE = s / √n) — how much your sample mean would wobble on repeat sampling, ready to report as x̄ ± SE.
In service MI-07-178Stem and Leaf Plot Calculator
Generate a stem-and-leaf plot from a list of numbers — a quick text-based way to see a dataset's shape while keeping every individual value visible.
In service MI-07-179Sum of Squares Calculator
Compute the sum of squared deviations from the mean (SS) — the raw ingredient behind variance, standard deviation and ANOVA — with the working shown.
In service MI-07-180t-statistic Calculator
Calculate the one-sample t-statistic, t = (x-bar − mu0) / (s / sqrt(n)) — how many standard errors your sample mean sits from a hypothesized value.
In service MI-07-181t-test Calculator
Compare two independent sample means with the pooled-variance t-test — enter each group's mean, standard deviation and size to get the pooled t-statistic.
In service MI-07-182Third Quartile Calculator
Find Q3, the value above which the top quarter of your data sits — a single cut point, computed by linear interpolation and shown with the working.
In service MI-07-183Two Dice Probability Calculator
Find the probability of rolling a specific sum (2 through 12) on two standard six-sided dice, and how many of the 36 equally likely combinations produce it.
In service MI-07-184Two Envelopes Paradox Calculator
Work through the two-envelopes paradox — the naive 1.25x switching argument computed for any amount, and why it's a logical trap, not real winning advice.
In service MI-07-185Uniform Distribution Calculator
Find the continuous uniform distribution's density, cumulative probability, mean and variance between bounds a and b, where every outcome is equally likely.
In service MI-07-186Upper and Lower Fence Calculator
Get both outlier boundaries at once — lower fence = Q1 − 1.5 × IQR and upper fence = Q3 + 1.5 × IQR — everything a box plot's whiskers need from one data set.
In service MI-07-187Upper Control Limit Calculator
Calculate the upper control limit (UCL) for a process control chart from mean, standard deviation, and subgroup size — the classic 3-sigma out-of-control line.
In service MI-07-188Upper Fence Calculator
Calculate the upper fence, Q3 + 1.5 × IQR — the boundary above which a value counts as an unusually high outlier, using the standard box-plot rule.
In service MI-07-189Variance Calculator
Calculate sample variance (s²): the average squared distance of your data from its mean, corrected for sampling bias by dividing by n minus 1.
In service MI-07-190Venn Diagram Calculator
Calculate the union and the exclusive-only regions of two overlapping sets from their sizes and overlap — the arithmetic behind every two-circle Venn diagram.
In service MI-07-191Weibull Distribution Calculator
Find the Weibull distribution's density f(x) and cumulative probability F(x) from shape k and scale λ — the standard model for time-to-failure.
In service MI-07-192Wilcoxon Rank-Sum Test Calculator
Calculate the Wilcoxon rank-sum statistic (W) and its z-approximation from two samples — a nonparametric test comparing groups without assuming normal data.
In service MI-07-193Youden Index Calculator
Calculate Youden's J index from a confusion matrix: enter TP, FP, TN, FN to combine sensitivity and specificity into one diagnostic-performance score.
In service MI-07-194Z-score Calculator
Enter a raw value, a mean and a standard deviation to get the z-score — how many standard deviations that value sits above or below average.
In service MI-07-195Z-test Calculator
Test a sample mean against a hypothesized value with the one-sample z-test, z = (x-bar − mu0) / (sigma / sqrt(n)), for when population sigma is known.
In serviceOn the Board
16 catalogued · not yet builtThese sheets are numbered and queued. They are listed for transparency about what this series will contain — they are not links yet, because nothing here ships before its formula is verified twice.
- MI-07-002 10 Sided Dice Roller Calculator
- MI-07-003 2 Dice Roller Calculator
- MI-07-004 4-Sided Dice Roller Calculator
- MI-07-007 6 Sided Dice Roller Calculator
- MI-07-036 Coin Flipper
- MI-07-051 Custom Dice Roller Calculator
- MI-07-052 D100 Dice Roller Calculator
- MI-07-053 D20 Dice Roller Calculator
- MI-07-056 Decimal Random Number Generator
- MI-07-060 Dice Roller Calculator
- MI-07-062 DnD Dice Roller Calculator
- MI-07-147 Quiz: Dice Average Calculator
- MI-07-148 Quiz: Lottery Calculator
- MI-07-149 Quiz: Simpson’s Diversity Index Calculator
- MI-07-150 Random Dice Roller
- MI-07-151 Random Number Generator