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I work at a learning center and this problem came up during a lesson. The student stared at it for a while, and after looking at it myself, I am also puzzled.

An average of 368 students attend each of Jinlow Elementary School's home soccer games. About how many students would attend eight home games?

JMoravitz
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Jonathan Hebert
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    It would help if you took the time to type the question. It is frustrating to click to load an image to read the question. It is even more so to have to tilt your head sideways since the image is not even oriented correctly. – JMoravitz May 24 '16 at 22:46
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    There are competing interpretations for what the question is asking for. If it is saying for example "each game 368 tickets are sold on average for a home soccer game. How many tickets are sold on average over the course of eight games." This follows from linearity of expectation. A completely different interpretation is: "How many students will have purchased tickets to attend all eight games" which is unanswerable without more information about the student population, independence of events, and distribution of ticket sales. Given it is labeled as arithmetic, it is likely the first. – JMoravitz May 24 '16 at 22:52
  • Another possibility (also unanswerable) is "how many students would attend at least one of the eight games"? – Robert Israel May 24 '16 at 22:54
  • I think this is an inexcusably bad way to write this question. I've gone through thousands of these with students and they were never written this badly. – Jonathan Hebert May 24 '16 at 22:57
  • I agree, the wording is horrible. – Robert Israel May 24 '16 at 22:58
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    You would be disturbed then by how many textbooks at elementary levels have problems that are written this ambiguously. Some of these books are dashed off by publishing outfits which are written by "authors" with weak grasps of the subject and of decent pedagogy... Just out of curiosity, does the source provide an "answer"? That may help in interpreting the intent of the question (no promises). – colormegone May 24 '16 at 23:33
  • This is better suited to Mathematics Educators StackExchange. – M. Vinay May 25 '16 at 04:08

2 Answers2

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Each home game has, on average, 368 students attending. I think what it's asking you to do is simply multiply that average per game times eight games, i.e., $$368\text{ $\frac{\text{students}}{\text{game}}$ } \times 8\text{ games } = 2944\text{ students total.}$$

It is an oddly-worded question. However, with the information given (and for the grade level it's probably targeted towards), it seems to be asking for just the total attendance for the eight games, to have students realize that you can multiply the average of a list by the number of items in that list to get the sum.

gtmtg
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If $X_1,\dots,X_8$ are random variables each having expectation (or average) 368, $$ \mathbb E(X_1)=\dots=\mathbb E(X_8)=368, $$ then we have $$ \mathbb E(X_1+\dots+X_8)=8\times 368 = 2,944. $$

Bjørn Kjos-Hanssen
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