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If the set S is composed of the following numbers {99, 100, 100, 105,

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Bunuel
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If the set S is composed of the following numbers {99, 100, 100, 105, [#permalink] New post   15 Aug 2016, 04:03
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If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest?

A. The average (arithmetic mean) of set S
B. The median of set S
C. The mode of set S
D. The range of set S
E. The standard deviation of set S
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If the set S is composed of the following numbers {99, 100, 100, 105, [#permalink] New post   15 Aug 2016, 05:25
Bunuel wrote:
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest?

A. The average (arithmetic mean) of set S
B. The median of set S
C. The mode of set S
D. The range of set S
E. The standard deviation of set S


Time consuming question...

A) 99, 100, 100, 105, 106, 116, 123 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 123 -99 = 24.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n => sq root (64+49+49+4+1+676)/7 = sq rt ( 893/7) = sq rt ( 127) < 100

IMO option A is correct answer..

OA please..will correct if I missed anything..
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Re: If the set S is composed of the following numbers {99, 100, 100, 105, [#permalink] New post   15 Aug 2016, 19:13
Eyeballing through the set and the given options, the only true contenders are average and median. The values are around 100-110 so the answer must be close to that.

Range can be discarded as it is nowhere near 100 or 110.

Standard deviation can be discarded without any calculation. Standard deviation is the square root of the average of deviation of each value from the mean. The key word is square root. For standard deviation to be anywhere close to 100-110, the value inside the root needs to quite large and there is no way that can happen for the given set of values.

Median is the middle value. Since, we have 7 terms, median will be the 4th value -> 105.

Average:

Assume average is 100.
Get the "differential" of each term from the assumed average of 100 and add them up.
-1 + 0 + 0 + 5 + 6 + 16 + 23 = 49.
Since there is an extra 49, it needs to be evenly distributed among the 7 members.
49 / 7 = 7.
Add 7 back to the assumed average.

Actual average = 100 + 7 = 107.

107 > 105 or Average > Median.

Answer (A).
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Re: If the set S is composed of the following numbers {99, 100, 100, 105, [#permalink] New post   20 Jun 2020, 13:31
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Bunuel wrote:
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest?

A. The average (arithmetic mean) of set S
B. The median of set S
C. The mode of set S
D. The range of set S
E. The standard deviation of set S


Solution:

The correct answer is A or B since the mode is 100, which is obviously less than the median. The range is 123 - 99 = 24, which is even less than mode. As for the standard deviation, whatever it is, it’s less than the range. We see that the median is 105. Instead of calculating exactly what the average is, let’s compare each term with 105 (i.e., the difference with 105):

-6, -5, -5, 0, 1, 11, 18

We see that the sum of the negative numbers is -16 and the sum of the positive numbers is 30. This means the average must be greater than the median. (Note: If the two sums are equal in absolute value, then average = median. If the former sum (in absolute value) is greater than the latter sum, then average < median.)

Answer: A
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Re: If the set S is composed of the following numbers {99, 100, 100, 105, [#permalink]
20 Jun 2020, 13:31
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