On Wed, 02 Jan 2008 15:22:49 -0600, -Lost
<maventheextrawords@[EMAIL PROTECTED]
> wrote in
<news:Xns9A19A6E87C236lostthreads@[EMAIL PROTECTED]
> in
alt.algebra.help:
[...]
> Anyway, one problem that perplexed me slightly was:
> Mark took a French exam that consisted of 50 questions.
> He got an 80% on 15 true or false questions and a 60% on
> 35 multiple choice questions.
> I couldn't figure it out, but ended up guessing that it was 70.
You haven't actually told us what the question was, but your
comments suggest that you were to find Mark's overall
percentage score. If so, you can do it as follows.
80% of 15 is 0.8 * 15 = 12, so he got 12 of the 15
true-false questions right. 60% of 35 is 0.6 * 35 = 21, so
he got 21 of the 35 multiple choice questions right. Thus,
out of the 50 questions he got altogether 12 + 21 = 33
questions right; 33/50 = 0.66, so he got 66% of the
questions right.
[...]
> So is it just the average of the 2 scores? [...]
No: it's the *weighted* average of the two scores. An
ordinary average gives equal weight to the two scores.
Here, though, there are more multiple choice questions, so
the 60% on the multiple choice questions has more effect on
the overall percentage than the 80% on the true-false
questions. In fact 70% (35/50) of the exam is multiple
choice, and only 30% (15/50) is true-false, so the score on
the multiple choice questions accounts for 70% of the
overall score, and the score on the true-false questions
accounts for only 30%:
70% of 60% + 30% of 80% =
0.7 * 60% + 0.3 * 80% =
42% + 24% =
66%,
the figure we got before by actually calculating how many
questions he got right.
Brian
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