Percentages · 3 min read
Percentage of a Number: the method, worked through
A percentage describes a share of a chosen base.
30 illustrated guides
Number notes
Work through the formula, compare a few scenarios and know where the model stops.
Percentages · 3 min read
Understanding percentage change
Percentage change measures movement relative to the starting value.
Percentages · 3 min read
Percentage Difference: from inputs to a useful answer
When neither observation is a natural baseline, the arithmetic average gives a symmetric denominator.
Percentages · 3 min read
A practical guide to reverse percentage
Recover an original quantity after a known proportional increase.
Percentages · 3 min read
How discounted value works
A discount is a reduction from the original amount.
Percentages · 3 min read
Successive Changes: the method, worked through
Successive percentage changes compound because the second acts on an already changed base.
Percentages · 3 min read
Understanding part as a percentage
Express a measured part as a share of a reference total.
Percentages · 3 min read
Percentage Point Gap: from inputs to a useful answer
A percentage point gap subtracts two already expressed percentages.
Averages · 3 min read
A practical guide to weighted two-value mean
Weighted averages give observations influence in proportion to their weights.
Averages · 3 min read
How mean of three values works
The arithmetic mean balances three observations equally.
Averages · 3 min read
Median of Three Values: the method, worked through
The median is the middle observation in sorted order.
Averages · 3 min read
Understanding geometric mean
The geometric mean averages positive multiplicative factors.
Averages · 3 min read
Harmonic Mean: from inputs to a useful answer
The harmonic mean handles rates applied to equal quantities, such as equal distances traveled at two speeds.
Statistics · 3 min read
A practical guide to population variance
Variance measures the spread around the mean in squared units.
Statistics · 3 min read
How sample standard deviation works
Sample standard deviation expresses dispersion in the original measurement units.
Statistics · 3 min read
Population Standard Deviation: the method, worked through
Population standard deviation describes the spread of a complete three-observation set.
Statistics · 3 min read
Understanding z score
A z score expresses a distance from the mean in standard deviation units.
Statistics · 3 min read
Standard Error of Mean: from inputs to a useful answer
Standard error describes the sampling variability of a mean under independent sampling.
Statistics · 3 min read
A practical guide to coefficient of variation
The coefficient of variation describes dispersion relative to a positive mean.
Statistics · 3 min read
How range works
The range is the full span between the smallest and largest observations.
Averages · 3 min read
Root Mean Square: the method, worked through
Root mean square summarizes the magnitude of signed observations without allowing positive and negative signs to cancel.
Algebra · 3 min read
Understanding linear interpolation
Linear interpolation estimates a value on the straight line through two known points.
Algebra · 3 min read
Slope Between Points: from inputs to a useful answer
Slope compares vertical change with horizontal change.
Algebra · 3 min read
A practical guide to linear equation
Solve an equation of the form ax + b = c by undoing addition and multiplication in reverse order.
Algebra · 3 min read
How quadratic discriminant works
The discriminant indicates the real-root structure of a quadratic equation.
Algebra · 3 min read
Positive Quadratic Root: the method, worked through
This tool evaluates the plus branch of the quadratic formula for a real-coefficient equation.
Sequences · 3 min read
Understanding arithmetic sequence term
An arithmetic sequence adds the same difference at every step.
Sequences · 3 min read
Arithmetic Series Sum: from inputs to a useful answer
An arithmetic series adds a finite run of equally spaced terms.
Sequences · 3 min read
A practical guide to geometric sequence term
A geometric sequence multiplies by a constant ratio at every step.
Sequences · 3 min read
How geometric series sum works
The finite geometric sum combines a series of repeatedly scaled quantities.
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