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GRE Statistics
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Author:  questioner [ Tue Dec 18, 2012 8:26 am ]
Post subject:  GRE Statistics

Given the two lists:
List 1: 7, 8, 12, 15
List 2: 2, 10, 10, 13, 18

Indicate ALL correct answers.

The mean of List 1 > The mean of List 2
The median of List 1 > The mode of List 2
The standard deviation of List 1 > The standard deviation of List 2
The range of List 1 > The range of List 2
None of these is true.
--

The correct answer is None of these is true.

First, remember the definitions.
Mean (average) – sum of all elements of a set divided by the number of the elements.

Median – if the number of the elements in a set is odd, then it is the middle number of the set arranged in ascending or descending order;
if the number of the elements in the set is even, then it is the average of the two numbers in the middle of the arranged set.

Mode – the element(s) that appears most frequently.

Range – The largest element minus the smallest.

Let's look at each choice.

Choice A:
the mean of List 1 is (7 + 8 + 12 + 15)/4 = 42/4 = 10.5, and the mean of List 2 is (2 + 10 + 10 + 13 + 18)/5 = 53/5 = 10.6.
False.

Choice B:
The median of List 1 is (8 + 12)/2 = 10, and the mode of List 2 is 10.
False.

Choice C:
It is not necessary to calculate the standard deviation. Just note that the data are much more spread about List 2, so its standard deviation is greater.
False.

Choice D:
The range of List 1 is (15 – 7) = 8 and the range of List 2 = (18 – 2) = 16.
False.

All of the first 4 answer choices are false. Therefore, Choice E, none of these is true, is correct.
----------
The median of List 1 is 11.

Author:  Gennadiy [ Tue Dec 18, 2012 8:34 am ]
Post subject:  Re: GRE Statistics

Quote:
The median of List 1 is 11.
The median of List 1 is 10

List 1: 7, 8, 12, 15

Median – if the number of the elements in a set is odd, then it is the middle number of the set arranged in ascending or descending order;
if the number of the elements in the set is even, then it is the average of the two numbers in the middle of the arranged set.

List 1 is arranged in the ascending order and has four elements, which is an even number. Therefore the median is the average of the two middle numbers, 8 and 12.
(8 + 12) / 2 = 10

P.S. The median outside of the high school mathematics can be defined in a different way, but in GMAT we use only the definition provided above.

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