Histogram

Tags

math

Is a graph used to represent continuous data. The key feature of a histogram is that the area of a bar is proportional to the frequency it represents.

When plotting a histogram you need to calculate the frequency density of each bar as the frequency divided by the length of the class (the spread that was measured).

| Speed || \( 0 < v \leq 40 \) | \( 40 < v \leq 50 \) | \( 50 < v \leq 60 \) | \( 60 < v \leq 90 \) | \( 90 < v \leq 110 \) | |-------------------|-----------------------|------------------------|------------------------|-------------------------|-------------------------| | Frequency || 80 | 15 | 25 | 90 | 30 | | Class Width || 40 | 10 | 10 | 30 | 20 | | Frequency Density || 2 | 15 | 25 | 3 | 1.5 |

For example, consider the distribution in tbl:hist-eg. If we plot this table as a histogram we get fig:hist-eg.

\begin{figure}
  \centering
  \begin{tikzpicture}
    \begin{axis}[
      ymin=0,ymax=3.5,
      ytick={0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5},]
      \addplot[ybar interval]coordinates{(0,2.0)(40,2.0)};
      \addplot[ybar interval]coordinates{(40,1.5)(50,1.5)};
      \addplot[ybar interval]coordinates{(50,2.5)(60,2.5)};
      \addplot[ybar interval]coordinates{(60,3.0)(90,3.0)};
      \addplot[ybar interval]coordinates{(90,1.5)(110,1.5)};
    \end{axis}
  \end{tikzpicture}
  \caption{A histogram for the data shown in \autoref{tbl:hist-eg}. Observe that the
area of each bar is equal to the frequency value for that class.}
  \label{fig:hist-eg}
\end{figure}