Graphs

Segmented bar graph

Displays the distribution of a categorical variable across different groups

How to draw a segmented bar graph

• Draw a single bar for each group with all bars reaching a total height of 100%

• Divide each bar into stacked segments

• The height of each segment represents the relative frequency of that category

How to interpret a segmented bar graph

• Look for an association between variables

• If the segments look identical across all bars, there is no association

• If the segment heights change noticeably from bar to bar, an association exists

Histogram

Displays the distribution of a single quantitive variable

How to draw a histogram

• Divide data into equal-width intervals (bins) on the x-axis

• Draw adjacent bars where the height represents the frequency or relative frequency of data points in that bin

• The bars must touch

How to interpret a histogram

• Shape (skewed, symmetric, bimodal)

• Outliers (gaps)

• Center (estimate median/mean)

• Spread (range)

Stem-and-leaf plot

Displays quantitative data while preserving the individual raw data values

How to draw a stem-and-leaf plot

• Split each data point into a “stem” (leading digits) and a “leaf” (final digit)

• List stems vertically and leaves horizontally in vertical order

• You must include a key (e.g. 4|2 = 42 years old)

How to interpret a stem-and-leaf plot

• Shape (skewed, symmetric, bimodal)

• Outliers (gaps)

• Center (mean/median)

• Spread (range)

Boxplot

Visually displays the five number summary (Min, Q₁, median, Q₃, Max)

How to draw a boxplot

• Draw a central box from Q₁ to Q₃ with a vertical line at the median

• Calculate outliers using the 1.5 x IQR rule

• Mark outliers as isolated dots

• Extend “whiskers” from the box to smallest and largest non-outlier data points

Cumulative relative frequency graph

Displays the running total percentage of a quantitative variable as you move left to right

How to draw a cumulative relative frequency graph

• Plot the upper boundary of each data interval on the x-axis and the cumulative percentage on the y-axis

• Connect the points with line segments

• The graph always starts at 0% and ends at 100%

How to interpret a cumulative relative frequency graph

• Locate a percentage on the y-axis, move horizontally to the line, and look straight down to find the raw score

• Steep sections mean lots of data points are concentrated there

• Flat sections mean very few data points

Dotplot

Displays the distribution of a small quantitative dataset

How to draw a dotplot

• Draw a single, labeled horizontal axis

• Place one dot directly above the axis for every individual data value in the set

• Stack duplicate values vertically

How to interpret a dotplot

• Shape (skewed, symmetric, unimodal)

• Outliers (gaps)

• Center (mean/median)

• Spread (range)

Bar graph

Used for a single categorical variable