 ## Statistics Calculators: (69) lessons

Analysis of Variance (ANOVA)
Performs 1 way analysis of variance or 2 way analysis of variance on a set of data with critical value test and conclusion.
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Basic Statistics
Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ2
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
Highly Suspect Outliers
Stem and Leaf Plot
Ranked Data Set
Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range
Root Mean Square
Weighted Average (Weighted Mean)
Frequency Distribution
Successive Ratio
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Bayes Rule
Calculates the conditional probabilities of (B given A) of 2 events and a conditional probability event using Bayes Rule
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Benfords Law
Shows you Benfords Law and evaluates a data set compared to Benfords Law
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Bernoulli Trials
Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy
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Binomial Distribution
Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.
Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor
Calculates moment number t using the moment generating function
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Chebyshevs Theorem
Using Chebyshevs Theorem, this calculates the following:
Probability that random variable X is within k standard deviations of the mean.
How many k standard deviations within the mean given a P(X) value.
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Chi-Square χ2 Test
This calculator determines a χ2 chi-square test on a test statistic and determines if it is outside an accepted range with critical value test and conclusion.
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Chi-Square Critical Values
Given a probability, this calculates the critical value for the right-tailed and left-tailed tests for the Chi-Square Distribution. CHIINV from Excel is used as well.
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Class Frequency Goodness of Fit
Performs a goodness of fit test on a set of data with class boundaries (class boundary) with critical value test and conclusion.
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Coin Toss Probability
This calculator determines the following coin toss probability scenarios
* Coin Toss Sequence such as HTHHT
* Probability of x heads and y tails
* Probability of at least x heads in y coin tosses
* Probability of at least x tails in y coin tosses
* Probability of no more than x heads in y coin tosses
* Probability of no more than x tails in y coin tosses
* (n) Coin Tosses with a list of scenario results displayed
* Monte Carlo coin toss simulation
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Confidence Interval for the Mean
Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean
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Confidence Interval for Variance and Standard Deviation
Calculates a (95% - 99%) estimation of confidence interval for the standard deviation or variance using the χ2 method with (n - 1) degrees of freedom.
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Confidence Interval of a Proportion
Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion
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Confidence Interval/Hypothesis Testing for the Difference of Means
Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.
Also performs hypothesis testing including standard error calculation.
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Container Arrangements
Given a set of items inside a container, this calculates the probability that you draw certain items in the following fashion:
Draw all the items
Draw any of the items
How many ways can you choose m items of a, n items of b, o items of c, etc.
Calculator

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit
Given two distributions X and Y, this calculates the following:
* Covariance of X and Y denoted Cov(X,Y)
* The correlation coefficient r.
* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)
Exponential Fit
* Coefficient of Determination r squared r2
* Spearmans rank correlation coefficient
* Wilcoxon Signed Rank test
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Critical Values for F-test
Calculate a critical value for the F-Test statistic based on DF1, DF2, and α
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Critical Z-values
Given a probability from a normal distribution, this will generate the z-score critical value. Uses the NORMSINV Excel function.
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Difference of Proportions Test
Calculates a test statistic and conclusion for a hypothesis for the difference of proportions
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Event Likelihood
Given a probability, this determines how likely that event is
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Expected Frequency
Given a contingency table (two-way table), this will calculate expected frequencies and then determine a conclusion based on a Χ2 test with critical value test and conclusion.
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Expected Value
This lesson walks you through what expected value is, expected value notation, the expected value of a discrete random variable, the expected value of a continuous random variable, and expected value properties.
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Exponential Distribution
Calculates the Probability Density Function (PDF) and Cumulative Density Function (CDF) of the exponential distribution as well as the mean, variance, standard deviation, and entropy.
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Exponential Smoothing
Performs exponential smoothing on a set of data.
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F Test Statistic
Calculates the F-test statistic for two populations
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Favorable Outcome
Shows you various examples of favorable outcome in probability
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Fisher Transformation and Fisher Inverse
Given a correlation coefficient (r), this calculates the Fisher Transformation (z).
Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)
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Fishers Exact Test
Given a, b, c, and d, this calculates the probability of any such set of values using Fishers exact Test
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Frequency Distribution Table
Determines the classes and frequency distribution using the 2 to k rule.
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Fundamental Rule of Counting
Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.
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Geometric Distribution
Using a geometric distribution, it calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness, and kurtosis.
Calculates moment number t using the moment generating function
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Grand Mean
Calculates the grand mean of a set of number sets.
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Hypergeometric Distribution
Calculates the probability of drawing x objects out of a subgroup of k with n possibilities in a total group of N using the hypergeometric distribution.
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Hypothesis Testing for a proportion
Performs hypothesis testing using a test statistic for a proportion value.
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Hypothesis testing for the mean
Performs hypothesis testing on the mean both one-tailed and two-tailed and derives a rejection region and conclusion
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MAPE - MPE - MAPD
Given a time series of actual and forecasted values, this determines the following:
* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)
* Symmetric Mean Absolute Percentage Error (sMAPE)
* Mean Absolute Percentage Error (MPE)
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Margin of Error from Confidence Interval
Given a confidence interval, this determines the margin of error and sample mean.
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Mcnemar Test
Given a 2 x 2 contingency table and a significance level, this will determine the test statistic, critical value, and hypothesis conclusion using a Mcnemar test.
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Missing Average
Given a set of scores and an average, this calculates the next score necessary to attain that average
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Multinomial Distribution
Given a set of xi counts and a respective set of probabilities θi, this calculates the probability of those events occurring.
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Negative Binomial Distribution
Calculates the probability of the kth success on the xth try for a negative binomial distribution also known as the Pascal distribution.? ? It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, and standard deviation.
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Normal Distribution
Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability
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Odds Probability
Given an odds prediction m:n of an event success, this calculates the probability that the event will occur or not occur
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Odds Ratio
This calculator determines the odds ratio for 2 groups X and Y with success and failure for an outcome.
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P-Hat Confidence Interval
Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.
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Paired Means Difference
Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means
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Percentile for Normal Distribution
Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.
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Percentiles
Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.
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Point Estimate and Margin of Error
Given an upper bound and a lower bound and a sample size, this calculate the point estimate, margin of error.
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Poisson Distribution
Calculates the probability of 3 separate events that follow a poisson distribution.
It calculates the probability of exactly k successes P(x = k)
No more than k successes P (x <= k)
Greater than k successes P(x >= k)
Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.
Calculates moment number t using the moment generating function
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Probability
This lesson walks you through the basics of probability like the probability definition, events, outcomes, experiments, and probability postulates
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Probability (A U B U C)
Calculates the probability of a union of a three event sample space, A, B, and C, as well as P(A), P(B), P(C), P(A ∩ B), P(A ∩ C), P(B ∩ C), P(A ∩ B ∩ C).
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Probability (A U B)
Given a 2 event sample space A and B, this calculates the probability of the following events:
P(A U B)
P(A)
P(B)
P(A ∩ B)
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Proportion Sample Size
This calculator determines a sample size to select to meet certain criteria related to a confidence percentage, reliability percentage, and a p value proportion. Simply enter your values not using percentage signs. This works whether p^ is known or not known.
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Random Sampling from the Normal Distribution
This performs hypothesis testing on a sample mean with critical value on a sample mean or calculates a probability that Z <= z or Z >= z using a random sample from a normal distribution.
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Random Test
Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.
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Rule of Succession
Given s successes in n independent trials, this calculates the probability that the next repetition is a success
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Sample Size Reliability for μ
Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.
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Sample Size Requirement for the Difference of Means
Given a population standard deviation 1 of σ1, a population standard deviation 2 of σ2 a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.
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Sample Space Probability
Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.
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Sign Test
This will determine whether to accept or reject a null hypothesis based on a number set, mean value, alternative hypothesis, and a significance level using the Sign Test.
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Standard Normal Distribution
Givena normal distribution z-score critical value, this will generate the probability. Uses the NORMSDIST Excel function.
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Student-t Distribution Critical Values
Given an α value and degrees of freedom, this calculates the right-tailed test and left-tailed test critical values for the Student-t Distribution
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Tabular Display
Enter a set of x and p(x) in a tabular probability distribution format and this will evaluate if it is valid or not.
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Trimmed Mean and Winsorized Mean
Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.
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Uniform Distribution
This calculates the following items for a uniform distribution
* Probability Density Function (PDF) ƒ(x)
* Cumulative Distribution Function (CDF) F(x)
* Mean, Variance, and Standard Deviation
Calculates moment number t using the moment generating function
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Venn Diagram (2 circles)
Given two circles A and B with an intersection piece of C, this will calculate all relevant probabilities of the Venn Diagram.
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Z Score Lookup
Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.
* P(z < a)
* P(z <= a)
* P(z > a)
* P(z >= a)
* P(a < z < b) Calculates z score probability
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