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Median and mean

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Median and mean

by ricky01 » Sun Jul 24, 2016 8:05 am

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Is the median score for the set of children larger than the mean?

1) 70% of the students had a score more than 100
2) There are 500 students and the median is 350

Not sure about the answer, please help! tia
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Source: — Data Sufficiency |
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by MartyMurray » Sun Jul 24, 2016 1:50 pm

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B

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E

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You can do this one by using extreme values to make the mean and median high or low.

Statement 1: 70% of the students had a score more than 100.

Make the median low and the mean high.

30% - 100
69% - 101
1% - 1,000,000,000

Median = 101
Mean > 101

Mean > Median

Make median high and mean low.

30% - 0
70% - 200

Median = 200
Mean < 200

Mean < Median

Insufficient.

Statement 2: There are 500 students and the median is 350.

Make median low and mean high.

30% - 100
50% - 350
20%- 1,000,000,000

Median = 350
Mean > 350

Mean > Median

Make median high and mean low.

30% - 0
70% - 350

Median = 350
Mean < 350

Mean < Median

Insufficient.

Statements Combined:

Both scenarios for Statement 2 still work.

Insufficient.

The correct answer is E.
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by Matt@VeritasPrep » Fri Aug 19, 2016 3:32 pm

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ricky01 wrote:Is the median score for the set of children larger than the mean?

1) 70% of the students had a score more than 100
2) There are 500 students and the median is 350

Not sure about the answer, please help! tia
S1:

The median > 100.

The mean MIGHT be > 100, but it might not. (We could have 30 kids with scores of 0 and 70 with scores of 101.) Not sufficient!

S2:

No idea what the mean is, we could have students with scores of 1,000,000, or everyone could have a score of 350.

S1 + S2:

Let's borrow our reasoning from the first one. We could have 30*0 + 70*350, or we could have 30*99, 21*350, and 49*1,000,000. This gives us conflicting results, so we still don't know.
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