Cumulative Lines and Stem and Leaf Plots

Cumulative Lines and Stem and Leaf Plots

Cumulative line graphs are graphs that plot the cumulative frequency (on the y-axis) of a given variable (on the x-axis). These graphs are important if one wants to see how scores on a certain variable increase over time.

To create a cumulative line graph, you label your variable of interest on the x axis and the cumulative frequency on the y axis. For example, if you wanted to show the cumulative number of deaths per day from COVID-19, you would label the x-axis with the dates (representing the days of interest. On the y-axis, would represent the cumulative number of deaths. The last step is to plot the points on the graph and connect the points to make a line. You could use a frequency table to plot the cumulative frequency at each day. Finally, you connect the points and you have a cumulative line graph

Another graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.

For Susan Dean’s spring pre-calculus class, scores for the first exam were as follows (smallest to largest):

33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100

The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% were in the 90s or 100, a fairly high number of As.

Watch this video to see an example of how to create a stem plot, and see the links in the references for additional examples.

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