Data Measuring

Deviation

x - x̄ or x - μ, the difference between an individual value and the mean

A larger deviation

more spread out data

σ = sqrt( Σ(x - μ)² / N )

Population standard deviation

s = sqrt( Σ(x - x̄)² / n - 1)

Sample standard deviation

σ² = Σ(x - μ)² / N

Population variance

s² = Σ(x - x̄)² / n - 1

Sample variance

σ = sqrt( Σf(mi - μ)² / N )

Population standard deviation for grouped data

s = sqrt( Σf(x - x̄)² / n )

Sample standard deviation for grouped data

Σ|x - μ| / N

Population mean absolute deviation

Σ|x - x̄| / n

Sample mean absolute deviation

Σf|mi - μ| / N

Population mean absolute deviation for grouped data

Σf|mi - x̄| / n

Sample mean absolute deviation for grouped data

First quartile (Q1)

25th percentile of the data 0.25(n+1)

Second quartile (Q2)

50th percentile / Median of the data

Third quartile (Q3)

75th percentile of the data 0.75(n+1)

Interquartile range (IQR)

= Q3 - Q1

Percentile

k%(n+1)

Z = (x - μ) / σ

Z-score formula for population

Z = (x - x̄) / s

Z-score formula for sample

bi = μ + σZ

Bell mark formula for population

bi = x̄ + sZ

Bell mark formula for sample

N

Population size

n

Sample size

μ

Population mean

x̄

Sample mean

Outlier

Q1-IQRx1.5

Q3+1.5xIQR