Unit 15: Scatter Plots, Two-Way Tables, and Probability
Whether two quantities move together, how a table sorts two categories at once, and the chances behind combined events.
5 topics · 18 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Scatter Plots and Association
- How it worksHow do points clustering in a rising or falling pattern on a scatter plot show a positive, negative, or no association?
- Worked exampleGraph the data pairs 1 comma 65, 2 comma 70, 3 comma 78, and 4 comma 85 and describe the association you see.
- Common mistakeWhy doesn't a strong pattern on a scatter plot prove that one quantity causes the other to change?
Your turn1 of 2
A scatter plot of hours studied versus test score shows points rising from lower left to upper right. What kind of association is this?Line of Best Fit
- How it worksHow do you draw a line of best fit so it passes as close as possible to every point in a scatter plot?
- Worked exampleFind the test score predicted by the line of best fit y equals 5x plus 60, for 6 hours of studying.
- Common mistakeWhy doesn't a line of best fit need to pass through every single point, or even any of them, to be useful?
- Going furtherWhat happens to a prediction's reliability when you use a line of best fit far outside the range of the original data?
Your turn1 of 2
A class's line of best fit predicts test scores using y equals 6x plus 59, where x is hours studied. What score does it predict for 9 hours of studying?Two-Way Tables
- How it worksHow do the rows, columns, and totals of a two-way table organize counts of two categorical variables?
- Worked exampleFind what percent of 7th graders play soccer, using a two-way table of 50 students showing sport played and grade level.
- Common mistakeWhy doesn't a bigger raw count in one cell of a two-way table always mean a bigger percentage?
Your turn1 of 2
A two-way table shows that 14 out of 59 7th graders play soccer. What percent of 7th graders play soccer?Basic Probability
- How it worksHow does dividing the number of favorable outcomes by the total number of outcomes give you a probability?
- Worked exampleFind the probability of rolling a number greater than 4 on a standard six-sided die.
- Common mistakeWhy doesn't flipping four tails in a row make heads more likely on the next flip?
Your turn1 of 2
Ben rolls a standard six-sided die. What is the probability that it lands on a number greater than 4?Compound Events
- How it worksHow do you multiply the probabilities of two independent events to find the probability that both happen?
- Worked exampleFind the probability of rolling a 6 on a die and then flipping heads on a coin.
- Worked exampleFind the probability of drawing two red marbles in a row, with replacement, from a bag of 4 red and 6 blue marbles.
- Common mistakeWhy doesn't drawing a card and then a second card without putting the first one back use the same probability twice?
- Ties togetherHow does a two-way table's counts connect to the probabilities you calculate for compound events drawn from the same group?
Your turn1 of 2
Priya's bag has 7 red marbles and 6 blue marbles. What is the probability of drawing a red marble, then flipping heads on a coin?