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- Graph your data on Centimeter Grid Paper.
- Plot the total number of beans in the sample (n) on the horizontal axis and the number of tagged beans (t) in the sample on the vertical axis.
- If there are no beans in your sample, how many tagged beans will you find? (n = 0, t = ?) Add this point to your graph.
- If the points suggest a line, use a ruler to draw a best-fit line.
- If a sample has 100 beans (n = 100), how many tagged beans (t) would you expect in the sample? Use your graph to find t.
- If the number of tagged beans in a sample is 50 beans (t = 50), use your line to estimate the number of beans in the sample (n).
- Use your best-fit line to find the ratio (
) of the number of tagged beans in a sample to the total number of beans in the sample. (Hint: Choose a point on the line—not a data point—and find the values of t and n and write the ratio. For example, you may wish to use n = 100 and the value for t that you found in Question 16A.) - Choose another point on the line. Find the values for t and n for this point.
Write the ratio of using these values.
- Is this ratio equal to (or approximately equal to) the ratio you found in Question 16? How do you know?
- Find values for t and n for another point and write the ratio of . Is this ratio equal to (or approximately equal to) the other two ratios?
- Use a ratio from the line to calculate an estimate for the total number of beans in your bag. Use equivalent ratios to find N.
- Explain how you made your estimate. Use the Math Practices page in the Reference section.
