The main graphical methods for quantitative data are the histogram, frequency polygon, frequency curve, ogive, stem-and-leaf plot, box plot, scatter diagram and line (time-series) graph.
- Histogram: adjacent rectangles on class intervals with heights (or areas) proportional to frequencies. Shows the shape of the distribution. Example: marks of 50 students in classes 0–10, 10–20, ….
- Frequency polygon: class mid-points plotted against frequencies and joined by straight lines, closed at both ends on the x-axis. Handy for comparing two distributions on one chart.
- Frequency curve: a smoothed polygon showing patterns such as bell-shaped, skewed or bimodal.
- Ogive: cumulative frequency plotted against class boundaries. "Less than" ogive uses upper limits, "more than" ogive uses lower limits. Median, quartiles and percentiles can be read from it; the two ogives meet at the median.
- Stem-and-leaf plot: splits values into stem and leaf (e.g. 63 → 6 | 3), keeping original data while showing shape.
- Box-and-whisker plot: five-number summary (min, \(Q_1\), median, \(Q_3\), max); shows spread, skewness and outliers.
- Scatter diagram: plots paired values \((x, y)\) to show correlation.
- Line graph / time-series graph: values against time, showing trend, seasonal and cyclic movements, e.g. monthly rainfall or sales.
- Dot plot: each value shown as a dot above a number line; suitable for small data sets.
Rules for good graphs: a clear title, labelled axes with units, a suitable scale starting from zero for bars, and a legend where needed.
Uses: quick understanding of large data, comparing groups, detecting trends and outliers, and checking assumptions such as normality before analysis.