Data Graphs: Columns, Histograms, Dot Plots and Stem-and-Leaf

A column graph displays categorical data. Each category gets a column whose height is its frequency, and the columns have gaps between them because the categories are separate groups. All columns must be the same width, both axes need labels, and the graph needs a title. The rule that matters most is that the vertical scale must start at zero. Starting it at five instead would make a column of 11 look nearly twice as tall as one of 8, which is exactly how misleading graphs work — and advertisements do this deliberately. So whenever you read a graph, check the scale before you believe the picture.

A histogram looks similar to a column graph but is for numerical data, and there is one visible difference: no gaps between the bars. The bars touch because the number line runs continuously — nothing is missing between 154 and 155 centimetres, so there is no reason for a gap. Each bar sits over its class interval, and histograms are ideal for grouped continuous data such as heights, masses and times, because the shape of the distribution shows clearly. Gaps or no gaps is the whole difference: a column graph has gaps because the categories are separate, while a histogram has none. Drawing gaps on a histogram is a genuine error, not a style choice.

A dot plot puts one dot above the number line for each data value, stacking them. It suits small sets of discrete numerical data, and its strength is that every individual value stays visible — unlike a histogram, which groups values and loses them. You can read everything off it: the mode is the tallest stack, here 1 pet; the range is 4 minus 0, which is 4; and the total is simply all the dots counted, 20. Outliers show up immediately as lonely dots away from the rest. The limitation is size, since 200 values would need 200 dots. And stack the dots neatly in line, or the heights stop meaning anything.

A stem-and-leaf plot splits each value into a stem and a leaf — for two-digit numbers the stem is the tens and the leaf is the units, so 23 becomes stem 2, leaf 3. It is the only display that keeps every original value while also showing the shape of the data. Three rules: leaves must be in order smallest first, every leaf is a single digit, and a key is compulsory, because without one '2 bar 3' could mean 23 or 2.3. Because the values survive and are already sorted, you can find the statistics exactly. With ten values the median is the average of the fifth and sixth, both 34, so 34. The mode is 34 and the range is 51 minus 23, which is 28. A histogram could not give you any of those exactly.

Here are all four on one card. A column graph is for categorical data and has gaps between the columns. A histogram is for grouped numerical data and its bars touch. A dot plot suits small sets of numerical data, showing one dot per value. And a stem-and-leaf plot suits two-digit numerical values, keeping every value and requiring a key. Whichever you draw, four things are always required: a title, labelled axes, an even scale starting from zero, and a key where the display has one. Those four carry marks on their own, quite apart from whether the data is plotted correctly.