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Formula Sheets / Maths

Chapter 31

Statistics

Revise with flashcards Download this chapter (PDF) All Maths formulas (PDF)

Mean, median and mode Mean deviation Variance and standard deviation

Mean, median and mode

Mean
$\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$
Median (grouped)
$M = l + \frac{\frac{N}{2} - C}{f} \times h$
Empirical relation
Mode $\approx 3$ Median $- 2$ Mean

Mean deviation

MD about $a = \frac{\sum f _{i} ∣ x _{i} - a ∣}{\sum f _{i}}$
Mean deviation is least about the median.

Variance and standard deviation

$σ^{2} = \frac{\sum f _{i} ( x _{i} - x ˉ ) ^{2}}{N} = \frac{\sum f _{i} x _{i}^{2}}{N} - \overset{x}{ˉ}^{2}$
Change of origin and scale
$y = a x + b : \overset{y}{ˉ} = a \overset{x}{ˉ} + b,$ $σ_{y} = ∣ a ∣ σ_{x}$
First n natural numbers
variance $= \frac{n ^{2} - 1}{12}$
Combined groups
$σ^{2} = \frac{n _{1} ( σ _{1}^{2} + d _{1}^{2} ) + n _{2} ( σ _{2}^{2} + d _{2}^{2} )}{n _{1} + n _{2}},$ $d_{i} = \overset{x}{ˉ}_{i} - \overset{x}{ˉ}$

Probability Mathematical Reasoning