Line Plot of Plant Heights
A class measures bean plants to the nearest quarter inch and records the heights on a line plot. The data are: 2, 2 1/4, 2 1/4, 2 1/2, 2 3/4, 2 3/4, 2 3/4, 3, 3, 3 1/4. A student says the "average" height is 3 inches because 3 appears twice and "most plants are around there." Another student wants to add all heights and divide by 10 but is unsure how to add the mixed numbers. The teacher wants the class to find the true mean, identify the most common height, and decide whether the student's claim about 3 inches is reasonable.
1. Compute the mean height and identify the mode. Show your addition clearly.
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Convert to quarters of an inch to add reliably:
- 2 = 8/4 (one plant)
- 2 1/4 = 9/4 (two plants) → 18/4
- 2 1/2 = 10/4 (one plant) → 10/4
- 2 3/4 = 11/4 (three plants) → 33/4
- 3 = 12/4 (two plants) → 24/4
- 3 1/4 = 13/4 (one plant) → 13/4
Total in quarters: 8 + 18 + 10 + 33 + 24 + 13 = 106 quarters. So the sum is 106/4 = 26.5 inches. Divide by 10 plants: 26.5 ÷ 10 = 2.65 inches, or 2 13/20 inches.
The mode (most frequent height) is 2 3/4 inches, appearing three times.
2. Is the claim that "the average is 3 inches" reasonable? Support your judgment with the data.
Read the worked answer
No. The true mean is 2.65 inches, which is 0.35 inches below 3. The student confused frequency with average: 3 inches appears twice, but 2 3/4 appears three times, so even the mode is not 3.
The distribution is skewed low - five plants are below 2 1/2 inches, and only three reach 3 or higher. A quick sanity check: if every plant were 3 inches, the total would be 30 inches, but the actual total is 26.5 inches, so the mean must fall below 3. The claim is not reasonable; the mean of about 2.65 inches is the better summary, and the mode of 2 3/4 inches describes the most common height.