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Consider the following graph and the 7th and 8th statements.

enter image description here

For me, the 7th and 8th statements are ambiguous.

7th statement

  • If we consider the statement only by subtracting 13.2 from 18.9 which is 5.7 then the statement is true.

  • But if we calculate the percentage of increment by (18.9-13.2)/13.2 = 0.43 then the statement is false.

8th statement

  • If we consider the statement only by comparing 2 consecutive years then the statement is true.

  • However, if comparison can be performed on any pairs then the statement will be false because the most decrements occur between 1965 and 2001.

Questions

Do you think these 2 statements ambiguous? Or there are some conventions among Japanese that I miss here.

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7th statement

Yes, the 7th statement ("n percent increase from m percent") is ambiguous (between n+m percent and m*(100+n)/100 percent), and I believe a careful writer should never make a sentence like this.

The literal interpretation is the latter, but in reality, people who are not good at math often make a sentence like this. If I were forced to answer this question, I would answer "○ (true)" assuming the questioner is having 18.9 - 13.2 = 5.7 > 5 in mind. (But luckily, the answer will be true anyway, because (18.9-13.2)/13.2 = 0.43 is a 43% increase, which is larger than 5% (=0.05).)

To avoid the ambiguity, you should use ポイント(の上昇/低下/etc) to refer to the simple arithmetic difference of the two percentages. 「たばこを吸う女性の割合は5ポイント以上増えた」 always refers to 18.9 - 13.2 = 5.7 > 5.

  • 何%ではなく何ポイント上昇などというのは何故
  • Percentage point (English Wikipedia)
  • パーセント (Japanese Wikipedia)

    「支持率が50%から10%増加して60%になった」などという表現は誤用である。50%から10%の増加であれば、 0.50 + (0.50×0.10) = 0.55 = 55%だからである。正しくは「支持率が50%から10パーセントポイント増加して60%になった」と表記する。なお、「パーセントポイント」は単に「ポイント」と言われることも多く、日本では「パーセントポイント」と言われることは稀である。

8th statement

I think you can safely assume that the questioner is focusing on the increase/decrease happened in each 5-year section here. So you can calculate the difference of each adjacent pair of numbers (ie, 86.7-81, 81-76.3, 76.3-69.1, ...) and get the 5-year section where the difference is the largest.

  • Second paragraph, last sentence, "the 43% increase" ⇒ "a 43% increase" - Can I suggest edits for typos like this somewhere other than the comments? – sazarando Jul 6 '16 at 8:18
  • Thank you, you can always directly fix my simple errors without prior notice. (And let me do the same if I found a simple error in yours) – naruto Jul 6 '16 at 8:21
  • Don't you think that saying 「の間に」removes the mathematical ambiguity for Statement 7? Sort of like, the difference between these two statements in English: "a 5% increase from 1995 to 1998" and "a 5% difference between 1995 and 1998" – sazarando Jul 6 '16 at 8:23
  • I tried to make a change, but it said I need to change at least six characters and I didn't want to change anything but that one short word. Any other options in that case? – sazarando Jul 6 '16 at 8:24
  • No, the ambiguity for Statement 7 is not the matter of "plus or minus", but the matter of "subtraction or multiplication". You need 2000 reps to edit other answers. – naruto Jul 6 '16 at 8:35
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I think the ambiguity is taken away by two phrases in both statements:

  • 1985年から2001年の間に...5%以上増えた
  • ...もっとも大きく下がっているのは、1975年から80年にかけてである

The first statement indicates that what is being compared is only the difference between beginning percentage and final percentage for the date range given.

The second statement however, is comparing what happened "over a period of time" and logically may require more complex calculation than simply finding the difference between the beginning and end of the period in question.

There is no in-between data for this second statement in the graph though, so in this context finding the difference should be enough to determine the accuracy of the statement.

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