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DS - Average Range

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by karthikpandian19 » Thu Jun 28, 2012 11:51 pm
Is the average (arithmetic mean) of a certain set of m numbers, where m > 3, equal to the median of the set?

1. The range of the m numbers in the set is 5(m - 1).
2. If the m numbers in the set are listed in increasing order, the difference between any pair of successive numbers in the list is 5.

*****Help me understand / interpret the statement 1*****
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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Jun 29, 2012 12:03 am
karthikpandian19 wrote:Is the average (arithmetic mean) of a certain set of m numbers, where m > 3, equal to the median of the set?

1. The range of the m numbers in the set is 5(m - 1).
2. If the m numbers in the set are listed in increasing order, the difference between any pair of successive numbers in the list is 5.
Statement 1: Consider the following two sets
{0, 1, 2, 3, 20} --> m = 5 --> Range = (20 - 0) = 20 = 5*(5 - 1)
Mean ≠ Median

{0, 5, 10, 15, 20} --> m = 5 --> Range = (20 - 0) = 20 = 5*(5 - 1)
Mean = Median

Not sufficient

Statement 2: This means the numbers in the set are equispaced. Hence, mean will always be equal to median.

Sufficient

The correct answer is B.
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by karthikpandian19 » Fri Jun 29, 2012 12:09 am
To validate the statement 1, other than plugging in nos......is there any other method? (just out of curiosity)
Anurag@Gurome wrote:
karthikpandian19 wrote:Is the average (arithmetic mean) of a certain set of m numbers, where m > 3, equal to the median of the set?

1. The range of the m numbers in the set is 5(m - 1).
2. If the m numbers in the set are listed in increasing order, the difference between any pair of successive numbers in the list is 5.
Statement 1: Consider the following two sets
{0, 1, 2, 3, 20} --> m = 5 --> Range = (20 - 0) = 20 = 5*(5 - 1)
Mean ≠ Median

{0, 5, 10, 15, 20} --> m = 5 --> Range = (20 - 0) = 20 = 5*(5 - 1)
Mean = Median

Not sufficient

Statement 2: This means the numbers in the set are equispaced. Hence, mean will always be equal to median.

Sufficient

The correct answer is B.
Regards,
Karthik
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by Anurag@Gurome » Fri Jun 29, 2012 12:16 am
karthikpandian19 wrote:To validate the statement 1, other than plugging in nos......is there any other method? (just out of curiosity)
If you are asking for a algebraic approach, then no. There is not enough information to form some equation etc as in general neither mean nor median depends upon range. One can assume lot of things and prove that the statement is not sufficient. But I don't see any point in that.
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