notes
Statistical Formulae

Statistical Formulae

Measures of Central Tendency

  • Mean: x¯=1nx i \bar{x} = \frac{1}{n} \sum x_i

  • Median: value of data point at n+12\frac{n+1}{2}th position

  • Mode: most frequent value

  • Percentile: value of data point at p100(n+1)\frac{p}{100}(n+1)th position

  • Quartile: value of data point at q4(n+1)\frac{q}{4}(n+1)th position

Measures of spread

  • Variance: σ x 2=1n(x ix¯) 2=1nx i 2x¯ 2\sigma^2_x = \frac{1}{n} \sum (x_i - \bar{x})^2 = \frac{1}{n} \sum x_i^2 - \bar{x}^2

  • Standard Deviation: σ x=σ x 2=1n(x ix¯) 2=1nx i 2x¯ 2\sigma_x = \sqrt{\sigma^2_x} = \sqrt{\frac{1}{n} \sum (x_i - \bar{x})^2} = \sqrt{\frac{1}{n} \sum x_i^2 - \bar{x}^2}

  • Interquartile Range: Q 3Q 1Q_3 - Q_1

category: statistics