Bivariate Data Worksheets Grade 11

1. A researcher is studying the relationship between study time (x, in hours) and test scores (y, out of 100). After collecting data from 50 students, the regression equation is calculated as ŷ = 65.2 + 2.8x. The correlation coefficient is r = 0.76. What percentage of the variation in test scores can be explained by the linear relationship with study time?
2. Construct a two-way table for Sophia's survey of 200 students on preferred study method (visual, auditory, kinesthetic) and performance level (high, average, low). 48 students prefer visual and have high performance, 32 prefer visual and have average performance, 20 prefer visual and have low performance. 24 prefer auditory and have high performance, 36 prefer auditory and have average performance, 20 prefer auditory and have low performance. 8 prefer kinesthetic and have high performance, 12 prefer kinesthetic and have average performance, 0 prefer kinesthetic and have low performance. Calculate the marginal relative frequency of students who prefer visual study methods.
3. Create a scatter plot for Liam's data: (1,5), (5,13), (9,21), (13,29), (17,37), (21,45), (25,53), (29,61), (33,69), (37,77). Calculate the correlation coefficient r.

…and 3 more problems

1. Matiu surveyed 120 students at his school about their preferred study method (visual aids or reading notes) and their performance in a recent mathematics test. The two-way table below shows the results. Complete the two-way table by calculating the missing values and then determine if there is an association between study method preference and test performance. \begin{tabular}{|c|c|c|c|} \hline & Passed & Failed & Total \\ \hline Visual Aids & 45 & 15 & 60 \\ \hline Reading Notes & ? & ? & 60 \\ \hline Total & 70 & 50 & 120 \\ \hline \end{tabular} What are the missing values in the 'Reading Notes' row, and what do the conditional relative frequencies by row suggest about the relationship between study method and test performance?
2. A scatter plot shows the relationship between study hours (x) and test scores (y) for 50 students. The data points form an approximately linear pattern with a correlation coefficient of r = 0.85. The regression line equation is y = 3.2x + 65. If a student studies for 8 hours, what test score does the regression model predict?
3. Create a scatter plot for Tane's data: (12, 28), (16, 36), (20, 44), (24, 52), (28, 60), (32, 68), (36, 76), (40, 84), (44, 92), (48, 100). Calculate the correlation coefficient r.

…and 3 more problems

1. Sophia, a high school science student, is investigating whether there is a relationship between the number of hours students spend on social media per week and their average exam score (out of 100). She surveys 30 students and records the following bivariate data. The data is summarized in the two-way table below, where hours on social media per week is categorized as Low (0–7 hours), Medium (8–14 hours), or High (15+ hours), and exam score is categorized as Low (below 70), Medium (70–84), or High (85–100). | Exam Score → | Low | Medium | High | Total | |--------------|-----|--------|------|-------| | Low Social Media | 2 | 7 | 5 | 14 | | Medium Social Media | 4 | 6 | 2 | 12 | | High Social Media | 3 | 1 | 0 | 4 | | Total | 9 | 14 | 7 | 30 | Based on this table, what percentage of students who spend High hours on social media scored in the High exam score category? Express your answer as a percentage (rounded to one decimal place, if necessary).
2. A medical researcher is studying the relationship between daily exercise time (in minutes) and resting heart rate (in beats per minute) for adults. After collecting data from 50 participants, the researcher calculates a linear regression equation of ŷ = 72 - 0.15x, where x represents daily exercise time and ŷ represents predicted resting heart rate. The correlation coefficient is -0.68. If a new participant exercises for 40 minutes daily, what would be their predicted resting heart rate according to this model?
3. Construct a two-way table for Kaia's survey of 75 students: 33 prefer online learning, 17 prefer in-person learning, and 25 are undecided. Among those who prefer online, 21 are female; among those who prefer in-person, 9 are male; among the undecided, 13 are female. Determine the number of male students who are undecided.

…and 1 more problems