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Dropdown 1: 30°C to less than 35°C
Dropdown 2: 20°C to less than 25°C
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Difficulty:
55%
(hard)
Question Stats:
74%
(02:21)
correct 26%
(03:06)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
A materials laboratory tested 56 adhesive samples, 28 made with Formula X and 28 made with Formula Y. The samples were cured within four temperature ranges: at least 20°C but less than 25°C, at least 30°C but less than 35°C, at least 40°C but less than 45°C, and at least 50°C but less than 55°C. Within each temperature range, 7 samples of each formula were tested. The graph shows the curing temperature and bond strength, in megapascals (MPa), for each sample.
Based on the information provided, select from each drop-down menu the option that completes the statement most accurately.
The median bond strength of Formula X exceeded the median bond strength of Formula Y by the greatest amount for samples cured at .
Formula Y had a greater range of bond strengths than Formula X only for samples cured at .
A materials laboratory tested 56 adhesive samples, 28 made with Formula X and 28 made with Formula Y. The samples were cured within four temperature ranges: at least 20°C but less than 25°C, at least 30°C but less than 35°C, at least 40°C but less than 45°C, and at least 50°C but less than 55°C. Within each temperature range, 7 samples of each formula were tested. The graph shows the curing temperature and bond strength, in megapascals (MPa), for each sample.
Based on the information provided, select from each drop-down menu the option that completes the statement most accurately.
The median bond strength of Formula X exceeded the median bond strength of Formula Y by the greatest amount for samples cured at .
Formula Y had a greater range of bond strengths than Formula X only for samples cured at .
Official Solution:
Drop-down 1:
The median is the middle value when the values are arranged from lowest to highest. Since there are 7 samples of each formula in each temperature range, the median is represented by the 4th-highest, or equivalently the 4th-lowest, point for that formula.
Scanning the graph, in the 30°C to less than 35°C range, the 4th-highest Formula X triangle is much higher than the 4th-highest Formula Y square. The vertical distance between these two middle points is greater than in any of the other temperature ranges, where the corresponding middle triangle and square are closer together.
Therefore, the median bond strength of Formula X exceeded that of Formula Y by the greatest amount for samples cured at 30°C to less than 35°C.
Drop-down 2:
The range is the difference between the highest and lowest values. On the graph, it is represented by the vertical distance from the lowest point to the highest point for a formula within a temperature range.
In the 20°C to less than 25°C range, the lowest Formula Y square is below the lowest Formula X triangle, while the highest Formula Y square is above the highest Formula X triangle. Thus, the Formula Y points span a greater vertical distance than the Formula X points, so Formula Y has the greater range.
Therefore, Formula Y had a greater range only for samples cured at 20°C to less than 25°C.
Correct answer:
Drop-down 1: "30°C to less than 35°C" Drop-down 2: "20°C to less than 25°C"