Bean Plant Line Plot
A class measured bean plants to the nearest 1/4 inch. The line plot shows these heights in inches: 2 1/4 (three plants), 2 1/2 (five plants), 2 3/4 (two plants), 3 (four plants), and 3 1/4 (one plant). The class wants to find the total height if all plants were laid end to end, and the difference between the tallest and shortest plant. A student, Devon, says the total is just the average height times 15 because there are 15 plants, but he cannot find the average. Another student says you cannot add mixed numbers with different fractions without a line plot. The teacher wants a table of heights, frequencies, and total inches, and a written explanation of how the fractional parts combine. The class also needs to decide whether the total is closer to 40 inches or 41 inches.
1. Make a table and compute the total height of all 15 plants. Show how you combine the fractional parts.
Read the worked answer
| Height (in.) | Frequency | Total height |
|---|---|---|
| 2 1/4 | 3 | 6 3/4 |
| 2 1/2 | 5 | 12 1/2 |
| 2 3/4 | 2 | 5 1/2 |
| 3 | 4 | 12 |
| 3 1/4 | 1 | 3 1/4 |
Add the totals: 6 3/4 + 12 1/2 + 5 1/2 + 12 + 3 1/4 = 40 inches. Another way: whole-number parts give 6 + 10 + 4 + 12 + 3 = 35; fractional parts give 3/4 + 2 1/2 + 1 1/2 + 0 + 1/4 = 5; and 35 + 5 = 40. So the total is exactly 40 inches, closer to 40 than to 41.
2. Find the difference between the tallest and shortest plant, and explain whether it is closer to 3/4 inch or 1 inch.
Read the worked answer
Tallest = 3 1/4 inches; shortest = 2 1/4 inches. Difference = 3 1/4 − 2 1/4 = 1 inch. On the line plot, the distance from 2 1/4 to 3 1/4 is four quarter-inch intervals, and 4/4 = 1 inch. So the difference is exactly 1 inch, not closer to 3/4 inch.
3. Devon says total = average × 15. Without computing the average first, explain how the table total can be used to check his idea.
Read the worked answer
Devon’s formula is valid only if the average is the mean of all 15 heights. The table gives a total of 40 inches, so the mean is 40 ÷ 15 = 2 2/3 inches. That mean is between the shortest height (2 1/4) and the tallest (3 1/4), which is a reasonable check. But the formula does not save work here because the average is not given; you still need the total from the frequency table. Checking back, 2 2/3 × 15 = 40, so the table total and the average are consistent.