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8: Graph Interpretation

Students read, interpret, and compare graphical data displays including box plots, histograms, scatterplots, bar charts, ROC curves, and Kaplan-Meier survival plots.

Box Plot Matching

Click to show Box Plot Matching example problem
A sample of N = 40 observations is summarized by the cumulative frequency table below.
Value Cumulative count
3 11
5 20
9 26
12 36
15 40
Quartiles use Tukey hinges: for rank k, choose the smallest value whose cumulative count is at least k; for even N, average the two middle ranks in each half (Q1: k=10,11; median: k=20,21; Q3: k=30,31), and ties are allowed.
Which box plot matches this cumulative frequency table?
 

Box Plots from Sorted Data

Click to show Box Plots from Sorted Data example problem
A sample of 11 measurements (already sorted) is shown below.
3, 3, 3, 3, 4, 6, 6, 6, 7, 8, 9
Which box plot correctly represents this data set?
Quartiles use Tukey hinges (median of halves); ties are allowed and keep the summary nondecreasing.
 

Box Plots from Five-Number Summary

Click to show Box Plots from Five-Number Summary example problem
A variable was summarized using the five number summary below.
Minimum = 6
Q1 = 9
Median = 9
Q3 = 11
Maximum = 11
Which box plot matches these summary statistics?
Quartiles use Tukey hinges (median of halves); ties are allowed and keep the summary nondecreasing.
 

Box Plots from Sample Data

Click to show Box Plots from Sample Data example problem
A sample of 12 measurements (unsorted) is shown below.
15, 18, 13, 16, 18, 18, 13, 18, 7, 11, 17, 9
Which box plot correctly represents this data set?
Quartiles use Tukey hinges (median of halves); ties are allowed and keep the summary nondecreasing.