Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of numerical data .

The two main statistical methodologies used in data analysis are descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation).

"Applied statistics" comprises descriptive statistics and the application of inferential statistics. Theoretical statistics concerns both the logical arguments underlying justification of approaches to statistical inference, as well encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

vCalc's Statistics library concerns equations that deal with the analysis , organization and interpretation of data.

Statistics Equations

• average (mean)
• Binomial Coefficient
• Chebyshev's Inequality(1)
• Chebyshev's Inequality(2)
• Circular r-Permutation of n Elements
• Coefficient of variation
• Conditional Probability of B given A
• Count
• Expected Value(Geometric)
• Expected Value(Pascal Distribution)
• Five Ear Sample Average
• Frequency Distribution
• Gamma Function
• least-squares trend line
• Maximum
• Mean
• Median
• Mid Point
• Minimum
• Observational Statistics
• P(event) = F / T
• P(n,S) - Bionomial Probability
• P(y) from z
• P(y) right of z
• Paired Samples t-test
• Percent Relative Standard Deviation
• Percentile
• Probability between raw scores
• Probability between z SCORES
• Random Sample (k items)
• Range
• Relative Standard deviation (RSD)
• Simple Stats
• Square of Sum
• Standard Deviation
• Standard deviation of mean
• Standard Error of the Mean (SEM)
• Statistical Mode
• Sum
• Sum of Squares
• t-test critical value lookup
• Variance
• Weighted Average
• y = a + bx
• y from P(y) Mean and SD
• z from P(y)
• z SCORE
• z SCORE formula
• Arithmetic Mean
• Arithmetic Mean (average)
• Arithmetic Mode
• Average number of kernels on five ears
• Batting Average
• Batting Average Against
• Bayes' Theorem for Disease Testing
• Bayes' Theorem for Event Probability
• Big Decimal Round
• Chebyshev's Inequality(1)
• Chebyshev's Inequality(2)
• Chi-Square (Stats)
• Chi-square goodness-of-fit test (C=3)
• Chi-squared test for association
• Choosing a Non-Parametric Test
• Choosing a Parametric Test
• Choosing a Relationship Test
• Coin Flip
• Competition Analysis
• Defense-Independent Component ERA
• Descriptive Statistics (n=10)
• Descriptive Statistics (n=11)
• Descriptive Statistics (n=12)
• Descriptive Statistics (n=6)
• Descriptive Statistics (n=7)
• Descriptive Statistics (n=8)
• Descriptive Statistics (n=9)
• Displaced Gaussian
• Earned Run Average
• Effect Size (r-squared)
• Efficiency
• Equivalent Average
• Expected Value(Bernoulli)
• Expected Value(Binomial)
• Expected Value(Discrete Uniform)
• Expected Value(Geometric)
• Expected Value(Hypergeometric)
• Expected Value(Pascal)
• Fielding Independent Pitching
• Fielding Percentage
• Free Throw Statistics
• Frequency Distribution
• Frequency Distribution (10 bin)
• Gaussian
• Gaussian Distribution
• Gaussian Distribution - Displaced
• Grades Card Frequency Distribution
• Happiness Probability
• Law of Total Probability P(A+B)
• Least Squares (n=3)
• Least Squares (n=4)
• Life expectancy [country]
• LittelWood's Law
• Lognormal
• Lognormal Distribution
• Mann-Whitney U test
• Matthews Correlation Coefficient
• Max
• Median
• Min
• Multiple Values from Gaussian Distribution
• Multiple Values from Gaussian Distribution (as string)
• Numeric Sort
• On-base Percentage
• On-base Plus Slugging
• One-way Analysis of Variance (ANOVA) - 3 Groups
• Paired Samples t-test (n=6)
• Pearson correlation (n=6)
• Performance Index Rating
• Probability of A and B
• Probability of A or B
• Probability of Non-independent Events (A, B)
• Pythagorean Expectation
• Random 0 OR 1
• Random Integer [0 , Upper]
• Random Integer [Lower , Upper]
• Random Real [0dot0, 1dot0]
• Random Real [0dot0, Upper]
• Random Real [Lower, Upper]
• Range
• Range Factor
• Rank Order Centroid
• Regression Line (n=6)
• regression test -- data set access (Weighted Geometric Mean)
• Relative Standard Deviation
• Repeated-measures Analysis of Variance (ANOVA) - 3 Groups
• Roll a 100-sided Virtual Dice
• Roll a 12-sided Virtual Dice
• Roll a 20-sided Virtual Dice
• Roll a 4-sided Virtual Dice
• Roll a 50-sided Virtual Dice
• Roll a 6-sided Virtual Dice
• Roll a 8-sided Virtual Dice
• Roll a D-100
• Roll Five Virtual Cube Dice
• Roll Four Virtual Cube Dice
• Simple Corn Yield
• Single-Sample t-test
• Slugging Percentage
• Spearman's rho correlation
• Stolen Base Percentage
• The Sorensen Coefficient
• Time of Death
• Times on Base
• Total Average
• Total Bases
• Variance (Population)
• Variance (Sample)
• Variance(Bernoulli)
• Variance(Bernoulli)
• Variance(Binomial)
• Variance(Binomial)
• Variance(Geometric)
• Variance(Geometric)
• Variance(Hypergeometric)
• Variance(Hypergeometric)
• Variance(Pascal)
• Variance(Pascal)
• Variance(Uniform)
• Variance(Uniform)
• Watts and Strogatz Degree Distribution
• Weighted Geometric Mean (bounded criteria)
• Weighted Geometric Mean (DataSet criteria)
• Weighted Geometric Mean (ten input criteria)
• Weighted Grade Average
• Wilcoxon signed rank test
• z-score
• z-score equation (find x)