Formulas for the Statistics Final
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Central Tendency
Mean
Median & Mode
𝑋=
Σ𝑋
𝑛
No formula
Variance
Population variance
Sample variance
2
2
Σ(𝑋−µ)
𝑁
2
Σ(𝑋−𝑋)
𝑛−1
σ =
𝑠 =
2
Standard deviation
Population standard deviation
σ =
2
2
Σ(𝑋−µ)
𝑁
σ =
Sample standard deviation
2
𝑠 =
Σ(𝑋−𝑋)
𝑛−1
d
Cohen’s d for one sample or
two samples
𝑑 =
𝑋−µ
or
σ
𝑑 =
z-scores
z-scores for a single score vs.
a population
𝑧 =
𝑋−µ
σ
z-scores for a single score vs.
a sample
𝑧 =
𝑋−𝑋
𝑠
=
𝑋−𝑀
𝑆𝐷
𝑋 1−𝑋
𝑠
𝑝
2
X from z
𝑋 = 𝑧 * σ + µ = 𝑧 * 𝑠 + 𝑋 = 𝑧 * 𝑆𝐷 + 𝑀
Regression
Predicting a raw score (X)
Y = intercept + slope * X
Y = b0 + b1*X
Predicting a z-score
zY = rxy * zX
(rxy = correlation between X and Y)