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. The scatter plot for these data is given below.
2. What conclusions can you draw from the scatter plot? 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 scatter plot. Interpret this line in context.
To create a quartile-quartile line, compute Q1 and Q3 for the horizontal axis (verify answers below). Separately compute Q1 and Q3 for the vertical axis (verify answers below). 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 |
\( y = \frac{19}{12} x - 7.96 = \frac{9.5}{6} x -7.96 = 1.5583 x - 7.96 \text{ using points } (14.5, 15) \text { and } (20.5, 24.5) \)
For everyone point that a student had on Exam I, they had approximately 1.5 points in Exam II.
Adapted from Which is better?
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?
\(y = \frac{21}{17.5} x - 17.2 = 1.2 x - 17.2 \text{ using points } (63.5, 59) \text{ and } (81, 80) \)
For everyone point the original had, the sequel had about 1.2 points.
2. Compute measures of center (mean, median, mode) for each data set. What conclusions can you draw from these values?
Original | Sequel | |
---|---|---|
Mean | 70.83 | 69 |
Median | 70 | 75 |
Mode | 64 | 75 |
Similar means. Median higher for sequels so some low scores must bring down mean. Mode?
3. Compute measures of variability (IQR, MAD, variance, standard deviation) for each data set. What conclusions can you draw from these values?
Original | Sequel | |
---|---|---|
IQR | 17.5 | 21 |
MAD | 11.17 | 12.33 |
variance | 178.31 | 217.17 |
SD | 13.35 | 14.74 |
Sequels had more variable data.
4. Create box plots, one for each exam on the same scale. What conclusions can you draw from the box plots?
Interpretation will vary.