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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 = σ^{2}

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

Expected Value

Mean = μ

Variance = σ

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

Chi-Square χ

This calculator determines a χ^{2} chi-square test on a test statistic and determines if it is outside an accepted range with critical value test and conclusion.

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.

Draw

Draw

How many ways can you choose m items of a, n items of b, o items of c, etc.

Derangements - Subfactorials

Calculates the number of derangements/subfactorial !n.

Function

Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.

Lagrange Four Square Theorem (Bachet Conjecture)

Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

Letter Arrangements in a Word

Given a word, this determines the number of unique arrangements of letters in the word.

Multiple Fractions (Addition or Ordering)

This adds 3 or more fractions or arranges a list of fractions from lowest to highest and highest to lowest (ordering fractions or sorting fractions)

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

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule

Percentile for Normal Distribution

Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

Permutations and Combinations

Calculates the following:

Number of permutation(s) of n items arranged in r ways =_{n}P_{r}

Number of combination(s) of n items arranged in r__unique__ ways = _{n}C_{r} including subsets of sets

Number of permutation(s) of n items arranged in r ways =

Number of combination(s) of n items arranged in r

Triangle Inequality

This calculator displays 2 scenarios

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

The domain of a relation is all even negative integers greater than -9. The range y of the relation

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H multiplied by 2x

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