Statistics formula sheet
31 formulas · what each one means · a free lesson for each
steplyclass.com/formula-sheets/statistics/ · free, step-by-step lessons for every formula
Center and spread
Mean of grouped data
x ≈ ΣfxΣf
x = the middle of each class, f = its frequency.Lesson: Mean of grouped data →Sample standard deviation
s = √Σ(x − x)2n − 1
Divide by one less than how many.Lesson: Standard deviation →Frequency density
frequencyclass width
The height of a bar when the classes are not the same width.Lesson: Histograms with unequal class widths →Lines of best fit
Line of best fit
ŷ = mx + b
It goes through the mean point (x̄, ȳ). ŷ (y-hat) is the predicted y.Lesson: Line of best fit →Correlation coefficient
r = Σ(x − x)(y − y)√Σ(x − x)2 × Σ(y − y)2
From −1 to 1: the sign gives the direction, near ±1 is strong.Lesson: The correlation coefficient →The normal curve
Margin of error (95%)
x ± margin
The true value is likely inside this interval.Lesson: Margin of error →Random variables
Sample means (CLT)
σx = σ√n
Means of big samples are normal, with a smaller spread.Lesson: Sample means and the central limit theorem →Confidence intervals
Mean, σ known
x ± z* × σ√n
z* = 1.645 (90%), 1.96 (95%), 2.576 (99%). The ± part is the error bound EBM.Lesson: Confidence interval for a mean →Hypothesis tests
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