Data Sufficiency

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

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.

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.