Bivariate data comparisons

Data for 18 students of a class is given below. Use these data for the given prompts.

Student Exam 1 Exam 2   Student Exam 1 Exam 2   Student Exam 1 Exam 2
Annabeth 15.5 11.5   Grover 14.5 21   Mason 18 14.5
Bianca 17.5 21   Hestia 21.25 25.75   Nico 19.5 20.75
Clarisse 14 18   Icarus 18.25 22   O'Leary 14.5 19
Dodds 12.25 14   Jason 16.5 12.5   Percy 16.75 18
Ethan 11.5 22.5   Kelli 19 26   Quintus 24.75 24.5
Fredrick 27.5 25   Luke 22.5 27   Rachel 20.5 15

1. Create a scatter plot for the data using Exam 1 and Exam 2 data on the axes. Another group member can find the quartiles of Exam 1. Yet another group member can find the quartiles for Exam 2.

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2. What conclusions can you draw from the scatterplot? Describe patterns such as clustering, outliers, positive or negative association, and linear or nonlinear association.


3. The data should have a slight positive association. Create a quartile-quartile line on the scatterplot. Interpret this line in context.

To do this, compute Q1 and Q3 for the horizontal axis. Separately compute Q1 and Q3 for the vertical axis. Find an equation of a line through the appropriate intersections.

  Q1 Median Q3
Exam 1 14.5 17.75 20.5
Exam 2 15 20.875 24.5


Sequels practice

Adapted from Which is better?

Metacritic scores for movies and their sequels
Movie series Original Sequel
Toy Story & Toy Story 2 92 88
Spider Man & Spider Man 2 73 83
Monsters Inc. & Monsters U 78 65
Night at the Museum & Night at the Museum: Battle for the Smithsonian 48 42
Shrek & Shrek 2 84 75
Star Wars & Empire Strikes Back 91 78
Pirates of the Caribbean: The Curse of the Black Pearl & Pirates of the Caribbean: Dead Man's Chest 63 53
X-MEN & X2 64 68
Harry Potter and the Philosopher's Stone & Harry Potter and the Prisoner of Azkaban 64 82
Princess Diaries & Princess Diaries 2 52 43
How to Train Your Dragon & How to Train Your Dragon 2 74 76
Hunger Games & Hunger Games Catching Fire 67 75

1. Assume a positive linear association. Find an equation for the quartile-quartile line for these data. What does this line mean in relationship to the table?

2. Compute measures of center (mean, median, mode) for each data set. What conclusions can you draw from these values?

3. Compute measures of variability (IQR, MAD, variance, standard deviation) for each data set. What conclusions can you draw from these values?

4. Create box plots, one for each exam on the same scale. What conclusions can you draw from the box plots?