The Statistics Calculator provides college level statistics functionality.    Frequency DistributionThis includes observation stats (min, max, mean, median, population and sample variance and standard deviation), sort, random sample, t-test, linear regression and more.  See the following:

• Observational Stats:  This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns.  This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
• Frequency Distribution:  This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins.  It then computes how many of the observations are in each of the bins between the high and low values designated. 
• Random Sample (k):  This generate a random sample of k items within a set.
• Percentile:  This computes the relative percentile of an observation verses a set.
• P(A) = F / T: This computes the probability of a favorable event in a total number of outcomes.
• P(n,S) - Binomial Probability:  Probability of S successes in n trials of a binomial distribution.
• B_C: - The binomial coefficient derived from Pascal's Triangle. 
• zSCORE (y in X):  This computes the z SCORE of an observation in a set (X).   Normal Distribution and z SCORES
• zSCORE (y,μ,σ):  This computes the z SCORE of an observation based on the mean and standard deviation.
• z from P(y):  This computes the z SCORE based on a probability or percentile in a Normal Distribution table.
• P(y) left of z: This computes the percentile, probability or area under the curve of a Normal Distribution left of the z SCORE.
• P(y) right of z: This computes the percentile, probability or area under the curve of a Normal Distribution right of the z SCORE.
• Probability between z SCORE:  This computes the area under the Normal Distribution curve between z SCOREs.
• Raw Score (P,μ,σ): This computes the raw score associated with a percentile in a Normal Distribution (μ,σ).
• Paired Sample t-test:  This computes the various parameters associated with the Paired Sample t-test.
• y = a + bx:  This is linear equation used with Linear Regression to predict values of Y.
• ANOVA (one way): The is one way analysis of variance
• (χ²) Chi-Square Test: This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.
• Linear Regression:  This computes the regression line (least-squares) through a set of X and Y observations.  It also computes the regression coefficient (r).              Linear Regression

The Math

The formulas for the statistics are as follows:

sum

     `S = sum_1^n(x)`

square of the sum

      (Σx)² = S²

sum of squares (Σx²)

      Σx² = `sum_1^n(x^2)`

averages

• mean:     `mu = (sum(x))/n`  where n is the number of observations
• median:  middle value if in an odd number of observations.  If there is an even number of observations, it's the average of the two middle values.
• mode:  the most repeated observation.
• mid-point:  `mp = (min + max)/2`

variance

• Population Variance: `sigma^2 = (sum_1^n(x_n-mu)^2)/n`
• Sample Variance:       `sigma^2 = (sum_1^n(x_n-mu)^2)/(n-1)`

standard deviation

• Population Standard Deviation:   `sigma = sqrt((sum_1^n(x_n-mu)^2)/n)`
• Sample Standard Deviation:         `sigma = sqrt((sum_1^n(x_n-mu)^2)/(n-1))`

Permutations

• Permutations:                                _nP_r = ` (n!)/((n-r)!)`
• Circular Permutations:                 P_c(n,r) = ` (n!)/(r(n-r)!)`
• Permutations with repetitions:   P_r(n) = n^r

Combinations

• Combinations:                                    _nC_k= ` (n!)/(k!(n-k)!)`
• Combinations with repetitions:      C_r(n, k) = ` ((n+k-1)!)/(k!(n-1)!)`

z SCORE

The formula for the z SCORE is as follows:

     `z_y =   (y - μ_X)/s`   where:

        - y is the single observation
        - μ is the mean
        - s is the sample or population standard deviation.

Least-squares Linear Regression

The formula for the least-squared regression line is in the following form:   y = a + bx

                      where:  `b = (  (sum(XY) - (sumX * sumY)"/n")) / (sum(X^2) - (sumX)^2"/n") `

                          and:  ` a = MY - b*MX`           MY is mean of Y.  MX is mean of X.

Statistics Calculators

• Stats Calc - Complete set of entry level college statistics functions
• Simple Stats - Complete set of Observational statistics for a set of data
• Linear Regression - Least-squares trend line for a set of data
• Chi-square Calculator
• One Way ANOVA - One way Analysis of Variance for three sets of data
• Count of Observations in a Set - this is the number (n) of values in a set.
• Minimum Value in a Set - this is the minimum observed value
• Maximum Value in a Set- this is the maximum value in the set.
• Numeric Sort (up and down) - this returns a comma separated list of the observations in ascending or descending order.
• Create a random subset of the a list of numeric values
• Random number from a range you specify
• Frequency distribution of data.
• Σx - this is the sum of the values in a set.
• Σx²  - this is the sum of the squared values
• (Σx)² - this is the square of the summed  values.
• Mean - the is the mean (average) of the observed values
• Median - the middle ordered value
• Mode - the most recurring observation
• Mid Point in a Set - this is the mid point of the observation range.
• Range in a Set  - this is the difference between the max and the min.
• Population Variance of the values
• Population standard deviation of the values
• Sample Variance of the values
• Sample Standard Deviation of the values
• Compute the z SCORE based on the mean and standard deviation
• Compute the z SCORE in a set of observations
• Compute the percentile of a single observation (y) in a set (X)
• SDOM - standard deviation of mean

Thanks

Thanks to Dr. Lee Hammerstrom, professor of math stats at Eastern Nazarene College and Dr. Richard (Rich) D. Platt, Associate Professor of Psychology at St Mary's College of Maryland, for their advice and testing.  Special thanks to Ms. Caroline Robertson for getting this library of equations off the ground.