Bar chart and histogram

Two charts that look very similar to the eye but are conceptually distinct serve to represent frequencies: the bar chart for discrete data and the histogram for continuous data.

Definition — Bar chart vs. histogram

• Bar chart: for discrete data (marks, genders, brands). Separated bars, the height is the frequency.
• Histogram: for continuous data grouped into classes (intervals). The rectangles are contiguous and the area of each represents the frequency: if the classes have different widths, the height must be the frequency density $h_i/\text{(width)}$, not $f_i$ directly (otherwise the eye overestimates the wide classes).

Example — Histogram of heights

Heights (in cm) of $20$ pupils grouped into classes of width $5$ cm: $[150,155){:}\,1, \quad [155,160){:}\,3, \quad [160,165){:}\,6, \quad [165,170){:}\,5, \quad [170,175){:}\,3, \quad [175,180){:}\,2.$

Histogram of the heights of 20 pupils, in classes of width 5 cm; the peak falls in the class $[160,165)$.

The peak in $[160,165)$ identifies the mode (modal class). The shape is slightly asymmetric to the right (positive skew).

Links

Topics: Probabilita
Concepts: Classi di frequenza · Grafico a barre · Istogramma · Moda
Methods: Istogramma
Skills: Interpretare grafico