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A large made-up test is taken by 200 students…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A large made-up test is taken by 200 students. The five-number summary of the marks is 12, 42, 55, 63 and 96. About how many students scored below 42? About how many scored between 42 and 63? About how many scored below 63? A student says, "The marks from 55 to 63 are crowded together, so fewer students are in that part than between 42 and 55." Is the student right?
Need a reminder? The key ideaShow
Sort the data. and are the medians of the lower and upper halves; with an odd count, leave the median out. The five-number summary is minimum, , median, , maximum.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Below . About a quarter of 200: 50 students.
Step 2. Between and . About half: 100 students.
Step 3. Below . About three quarters: 150 students.
Answer: about 50, 100 and 150 students.
The claim. The student is wrong. Each part between two of the five numbers holds about 50 students. A short part, such as 55 to 63, means the marks there are packed closely together, not that there are fewer of them.
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