Data displays are useful to aid with summarizing, analyzing, and interpreting a data distribution. The best data displays make useful information easy to read for the intended audience.

Frequency tables can be used to organize both categorical and numerical data.

Categorical data can be displayed using circle graphs or bar graphs.

In a circle graph, each piece represents the percentage or proportion of a category and all pieces add to 100\%.

In a bar graph, the height of each bar represents the frequency of that category.

Numerical data can be displayed using histograms, box plots, line plots, and stem-and-leaf plots.

Histograms and box plots are good for large quantities of data. The shape, center, and spread of the data is easy to read, but the individual data values are lost in these types of displays.

Histograms display the frequency of data as either a count or relative proportion along the y-axis and divide the numerical data into bins of equal width along the x-axis.

When constructing a histogram:

• There should be no gaps between the bars

• The bin range includes the value on the left side and excludes the value on the right side

• All bins should be the same width visually and numerically

Generally we exclude the lower bound and include the upper bound, so the equivalent labels for the x-axis would be:

Box plots divide data into four equal quartiles using the five-number summary: minimum, lower quartile, median, upper quartile, and maximum.

When constructing a boxplot:

• The box in the center represents the middle half and spread of the data

• The line in the box represents the median

• The two endpoints represent the minimum and maximum value

• The total count of data is not included in the box plot

Since every individual data point must be included in a line plot and stem-and-leaf plot these data displays are best for smaller data sets.

Line plots display the frequency of data by the number of dots at each value. This display is best used for discrete values with a small range.

When constructing a line plot:

• The number line must count by equal amounts with no gaps or "breaks"
• If a value on the number line is empty it means no data exist for that value
• Dots or X's represent each individual data point and should be stacked with equal size.

Stem-and-leaf plots organize data by place value to compare frequencies and are best for data values with a larger range.

When constructing a stem-and-leaf plot:

• In this case the "stem" represents the hundreds and tens digits together and the "leaf" represents the ones digit
• Both the stem column and each leaf row should be in increasing order
• No stem values can be skipped. If there is no data for that particular stem, the leaf column will have an empty row.

Worked examples