Bean Plant Data: A Line Plot, a Combined Strip, and a Visitor's Prediction
Each student in Ms. Okafor's class grew one bean plant from seed and measured it to the nearest 1/4 inch after three weeks. The 13 measurements, in inches, are:
2 1/2, 3, 3 1/2, 3 1/2, 3 3/4, 4, 4, 4 1/4, 4 1/2, 4 1/2, 5, 5 1/4, 5 1/2
Students will show the data on a line plot with a number line marked in quarter inches and one X per plant.
For the hallway display, the class will also lay paper strips end to end, one strip for each plant's height, to make a single long strip. The hallway case is 48 inches wide, and Ms. Okafor wants to know before taping whether the combined strip will fit.
A visitor looks at the numbers and predicts, 'Most of the plants must be between 4 and 5 inches, so the line plot will have its tallest stack in the middle.'
1. Find the total length of the combined strip in inches. Will it fit in the 48-inch case? Show a method that avoids converting every measurement to a fraction with a different denominator.
Read the worked answer
Add the whole inches and the fractional parts separately.
Whole inches: 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 = 49.
Fractional parts, counted in quarter inches: 1/2 = 2 quarters; 3/4 = 3 quarters; 1/4 = 1 quarter. The fractions present are 1/2 (three times), 1/2 again in the 3 1/2 pair and 4 1/2 pair, plus 3/4, plus 1/4 (twice). Counting all quarters: 2 + 0 + 2 + 2 + 3 + 0 + 0 + 1 + 2 + 2 + 0 + 1 + 2 = 17 quarters = 4 1/4 inches.
Total: 49 + 4 1/4 = 53 1/4 inches.
Fit check: 48 inches = 4 feet, so the strip is 53 1/4 − 48 = 5 1/4 inches too long.
Judgment: an estimate confirms this quickly - 13 plants averaging a bit over 4 inches is about 52–54 inches, definitely more than 4 feet. The class must fold the strip into two rows or shorten it.
2. Evaluate the visitor's prediction using the data and the structure of the line plot.
Read the worked answer
Count the plants from 4 inches through 5 inches, including both endpoints: 4, 4, 4 1/4, 4 1/2, 4 1/2, 5 - that is 6 of 13 plants. Six is not 'most'; a majority would need at least 7. The claim is false.
The second half of the prediction also fails. Stack heights in the line plot are the number of Xs at each value: 3 1/2 has 2 Xs, 4 has 2, 4 1/2 has 2, and every other value has 1. The tallest stacks are 2 Xs, and they occur at three different values, not in the middle. The plot would look nearly flat across the range from 2 1/2 to 5 1/2.
Judgment: the visitor estimated from the look of the numbers instead of counting. On a line plot, 'most' and 'tallest stack' must be read from the Xs, and the widths of the intervals matter - the data spread across the whole quarter-inch scale.
3. How much taller is the tallest plant than the shortest? How many plants grew at least 3 3/4 inches?
Read the worked answer
Range: tallest = 5 1/2 inches, shortest = 2 1/2 inches. Since the fractional parts match, subtract the whole numbers: 5 − 2 = 3 inches. (In quarter inches this is 22 quarters − 10 quarters = 12 quarters.)
At least 3 3/4 inches means 3 3/4 or more. Check each value against 3 3/4 = 3.75:
- 3 3/4 ✓, 4 ✓, 4 ✓, 4 1/4 ✓, 4 1/2 ✓, 4 1/2 ✓, 5 ✓, 5 1/4 ✓, 5 1/2 ✓ → 9 plants.
- Below the cutoff: 2 1/2, 3, 3 1/2, 3 1/2 → 4 plants.
Check: 9 + 4 = 13, matching the class size, so no plant was double-counted or skipped.
Judgment: 'at least' includes the boundary value, and plants exactly at 3 3/4 must be counted - a common error is to start the count at 4.