Percentages · 3 min read
Percentage of a Number: the method, worked through
A percentage describes a share of a chosen base.
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Percentage of a Number
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Percentages01
Percentage of a Number
A percentage describes a share of a chosen base.
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Percentage Change
Percentage change measures movement relative to the starting value.
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Percentage Difference
When neither observation is a natural baseline, the arithmetic average gives a symmetric denominator.
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Reverse Percentage
Recover an original quantity after a known proportional increase.
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Discounted Value
A discount is a reduction from the original amount.
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Successive Changes
Successive percentage changes compound because the second acts on an already changed base.
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Part as a Percentage
Express a measured part as a share of a reference total.
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Percentage Point Gap
A percentage point gap subtracts two already expressed percentages.
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Weighted Two-Value Mean
Weighted averages give observations influence in proportion to their weights.
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Mean of Three Values
The arithmetic mean balances three observations equally.
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Median of Three Values
The median is the middle observation in sorted order.
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Geometric Mean
The geometric mean averages positive multiplicative factors.
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Harmonic Mean
The harmonic mean handles rates applied to equal quantities, such as equal distances traveled at two speeds.
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Population Variance
Variance measures the spread around the mean in squared units.
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Sample Standard Deviation
Sample standard deviation expresses dispersion in the original measurement units.
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Population Standard Deviation
Population standard deviation describes the spread of a complete three-observation set.
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Z Score
A z score expresses a distance from the mean in standard deviation units.
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Standard Error of Mean
Standard error describes the sampling variability of a mean under independent sampling.
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Coefficient of Variation
The coefficient of variation describes dispersion relative to a positive mean.
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Range
The range is the full span between the smallest and largest observations.
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Root Mean Square
Root mean square summarizes the magnitude of signed observations without allowing positive and negative signs to cancel.
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Linear Interpolation
Linear interpolation estimates a value on the straight line through two known points.
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Slope Between Points
Slope compares vertical change with horizontal change.
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Linear Equation
Solve an equation of the form ax + b = c by undoing addition and multiplication in reverse order.
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Quadratic Discriminant
The discriminant indicates the real-root structure of a quadratic equation.
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Positive Quadratic Root
This tool evaluates the plus branch of the quadratic formula for a real-coefficient equation.
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Arithmetic Sequence Term
An arithmetic sequence adds the same difference at every step.
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Arithmetic Series Sum
An arithmetic series adds a finite run of equally spaced terms.
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Geometric Sequence Term
A geometric sequence multiplies by a constant ratio at every step.
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Geometric Series Sum
The finite geometric sum combines a series of repeatedly scaled quantities.
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Factorial
Factorial counts orderings of distinct objects.
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Permutations
Permutations count ordered selections without replacement.
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Combinations
Combinations count unordered selections without replacement.
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Binomial Probability
A binomial model describes a fixed number of independent trials with the same success probability on each trial.
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Independent Joint Probability
Multiply two probabilities to find their joint occurrence only when the events are independent.
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At Least One Success
The complement of no successes gives the chance of at least one success.
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Complement Probability
An event and its complement cover all outcomes without overlap.
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Expected Two-Outcome Value
An expected value is a probability-weighted average across two exhaustive outcomes.
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Odds to Probability
Odds in favor compare favorable outcomes to unfavorable ones.
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Uniform Interval Probability
A continuous uniform distribution allocates probability in proportion to interval length.
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Logarithm in Any Base
A logarithm asks which exponent raises the base to the target value.
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Nth Root
An nth root reverses raising a nonnegative value to an integer power.
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Ratio Scale
A proportional scale preserves a ratio while changing the reference quantity.
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Direct Proportion
Direct proportion keeps y divided by x constant.
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Inverse Proportion
Inverse proportion keeps the product of two quantities constant.
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Remainder
The remainder is what remains after fitting the largest whole number of divisor-sized groups into a nonnegative dividend.
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Greatest Common Divisor
The greatest common divisor identifies the largest exact shared grouping.
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Least Common Multiple
The least common multiple gives the smallest positive count divisible by both inputs.
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Distance on Number Line
Distance on a line removes direction and reports the separation of two signed positions.
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Midpoint on Number Line
The midpoint lies equally far from two positions on a straight number line.
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