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  • STA258 Pre-Lecture 02
  • ECO102 Lecture 01

Quartile

• These are percentiles / quantiles that divide ordered data into four equal parts.
• Quartiles:
  • Min: $0\mathrm{\%}$
  • Q1: $25\mathrm{\%}$
  • Q2: $50\mathrm{\%}$ $\to$ Median
  • Q3: $75\mathrm{\%}$
  • Max: $100\mathrm{\%}$
• The Inter-Quartile Range of the middle $50\mathrm{\%}$

\usetikzlibrary{decorations.pathreplacing, arrows.meta}
\begin{document}
  \begin{tikzpicture}[font=\sffamily]
    % Ligne numérique principale
    \draw[thick, -{Stealth}] (0,0) -- (10,0);
    
    % Boîte de l'écart interquartile (IQR)
    % On utilise 'color' pour la compatibilité TikZJax
    \draw[fill=blue!10, draw=blue!80, thick] (2.5, -0.6) rectangle (7.5, 0.6);
    
    % Ligne de la médiane (Q2)
    \draw[very thick, blue!80] (5, -0.6) -- (5, 0.6);
    
    % Tics et étiquettes pour les quartiles
    \foreach \x/\label in {1/Min, 2.5/$Q_1$, 5/$Q_2$, 7.5/$Q_3$, 9/Max} {
      \draw[thick] (\x, 0.1) -- (\x, -0.1);
      \node[below=8pt] at (\x, 0) {\small \label};
    }
    
    \draw[decorate, decoration={brace, amplitude=10pt, raise=5pt}, thick] (2.5, 0.6) -- (7.5, 0.6) 
      node[midway, above=18pt] {Inter-quartile range [IQR]};
      
    \node at (1.75, 0.3) {\tiny 25\%};
    \node at (3.75, 0) {\tiny 25\%};
    \node at (6.25, 0) {\tiny 25\%};
    \node at (8.25, 0.3) {\tiny 25\%};
    
  \end{tikzpicture}
\end{document}

• Inter-Quartile Range
• Range in Statistics
• Example:
  • $\begin{array}{cccc}1:109& 112& 114& 120\\ 2:126& 132& 141& 142\\ 3:147& 150& 152\end{array}$
  • It is ordered
  • $\text{Min}:109$
  • $Q_1:\frac{114+120}{2}=117$
  • $Q_2:132$ - Median
  • $Q_3:\frac{142+147}{2}=144.5$
  • $\text{Max}:152$
  • Inter-Quartile Range
  • $Q_3-Q_1=144.5-117=27.5$
  • $\text{Range}=152-109=43$