Statistics, Data, and Probability I: Drill Set 2, Problem 4. Which of the following statements is true?
|CAHSEE Math||Statistics, Data, and Probability I|
|Statistics||Charts, Graphs, and Tables|
|Statistics, Data Analysis, and Probability 6||Data sets|
So... when a question asks us anything like "which of the following are true",
it means we just have to roll up our sleeves and go one by one testing each little morsel
of hot dog they give us to evaluate. Let's just start with A.
It says, "more than half the students took between 15 and 45 minutes"
So then we just go back to the pie chart thing and see what it has to say.
Everything here is in percents, so to make things easier on ourselves, we can just think
about it as a number of students rather than some fancy fraction.
And in this case we can throw out answer A immediately because
57% took 45 minutes to an hour...
...that is, since over half DIDN'T fit in the 15 to 45 minute time window,
there's no way that more than half COULD.
We don't get brownie points for calculating that 10% took 15-30 minutes
and 23% took 30-45 minutes for a total of 33%.
So let's throw out A and move on as fast as we can.
B is sorta the counter-side of A.
It says LESS than half the students took 45 minutes to an hour to fnish...
...but we just noted that this number was 57% ... already OVER half.
So B is a quick easy toss out.
Move on to C.
C says: More than a quarter of the class took
EITHER 15 to 30 minutes to finish, OR did not finish the test at all.
So here, we've got a SUM. Meaning... we ADD both cases.
That's what happens when we have a conditional phrase like "OR".
As in... Hand me a condiment --
either that half gallon jug of ketchup OR that gallon jug of mustard.
So in the 15-30 minute group, we see that 10% of the students were captured here --
and then in the Did Not Finish group, we have 10% as well.
If we add them, we have a total of 20% of the students in those two groups.
So C is in fact only 20%, which is LESS than a quarter or 25%.
So C ain't cuttin' it for us either. Odds are very good D is the answer.
D says that more than a quarter of the class took between 15 and 45 minutes to finish.
Well, the 15-30 group was 10% - check.
And the 30-45 group was 23% - check.
ADD the two groups to get 33% and yeah -- woo hoo --
33% is in fact greater than a quarter or 25%
So the answer is, yes... we can read a pie chart. D.
Time for a slice.