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Description:
Statistics, Data, and Probability I: Drill Set 3, Problem 1. Which of the following statements is true?
Transcript
- 00:03
Here's another unshmoopy question for ya...
- 00:05
The graph below shows the results of the mayoral race for the town of Shmoopville.
- 00:11
Which of the following statements is true?
- 00:14
Here are the possible answers:
- 00:21
So... this is another "can you read a graph?" question.
Full Transcript
- 00:24
The question is asking us to compare the various answers as relative fractions or multiples
- 00:28
of each other. No short cuts here.
- 00:30
We have to actually identify a number with
- 00:32
each candidate -- that is, how many votes did each one get?
- 00:36
...and then just go one by one through the potential answers and ask... deal? Or no deal?
- 00:42
So let's start with candidate 1.
- 00:43
If we carefully note where the bar is, it stops at 13,000. Jot it down.
- 00:48
And while we're here, let's note the totals for the other candidates...
- 00:51
Candidate 2 got 26,000 votes,
- 00:53
Candidate 3 got 16,000,
- 00:55
and Candidate 4 got 29,000. And remember, this is in thousands of votes...
- 01:00
not millions, not tens, not dollars raised for their campaign, not number of political
- 01:04
favors... We are going to get a ton of curve balls thrown
- 01:07
at us, so we always need to make sure we're aware of exactly what these numbers represent.
- 01:12
Okay, now we just go back to potential answer A
- 01:14
and it says that candidate 4, with 29,000 votes...
- 01:17
...received twice as many as candidate 1,
- 01:20
who won 13,000 votes. Two times 13 is 26, not 29... so A is a big fat no... or false.
- 01:28
Potential answer B: candidate 2, at 26,000 votes, had 50% more votes than candidate
- 01:33
3, who had 16,000 votes. Well, 50% of 16 is the same as half of 16
- 01:39
which is 8... the questions asks for 50% MORE votes, so we'd add the 8 to the 16 and get
- 01:45
24 thousand votes. 24 does not equal 26 so B is also a big fat no.
- 01:52
Moving on.
- 01:53
Potential answer C: candidate 4 with 29,000 votes
- 01:56
won the election with about 35% of the total votes.
- 01:59
OK, a bit tricky here.
- 02:01
It's a two-parter. First, did candidate 4 win?
- 02:04
Well, yes she did -- the graph tells us that much. But we also have to figure out if she won
- 02:09
with about 35% of the TOTAL votes -- so we have to add up ALL the votes first...
- 02:14
If we add the votes for the 4 candidates, we see that the total votes in the election
- 02:19
were 13 plus 26 plus 16 plus 29... or 84,000 votes.
- 02:25
Is 29,000 about 35% of 84,000? It most certainly is!
- 02:30
So C is a definite yes here. And just to be sure D is wrong and we didn't
- 02:34
miss something, it's a good idea to do check that one, too
- 02:38
D is roughly the same as C, only it asks -- did Candidate 4 win with 50% of the votes?
- 02:43
Well, 50% of the votes of the total of 84,000 would be 42,000...
- 02:48
...so unless there were some Russian election "ballot helpers" there, candidate 4 only
- 02:53
had 29,000 votes, and was closer to that 35% figure.
- 02:57
As always, remember that the exam is asking us for the BEST answer, not always the perfect one.
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