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# In City X last April, was the average (arithmetic mean)

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In City X last April, was the average (arithmetic mean) [#permalink]  09 Jun 2010, 11:05
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In City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature?

(1) In City X last April, the sum of the 30 daily high temperatures was 2,160°.
(2) In City X last April, 60 percent of the daily high temperatures were less than the average daily high temperature.

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Last edited by Bunuel on 22 Jul 2012, 02:37, edited 1 time in total.
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Re: OG-DS - In City X [#permalink]  09 Jun 2010, 16:02
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In City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature?

Let's consider the temperatures in April in ascending order: $$t_1\leq{t_2}...\leq{t_{15}}\leq{t_{16}}\leq...\leq{t_{29}}\leq{t_{30}}$$. The median temperature would be the average of 15th and 16th greatest temperatures. The question asks: is this value less than the average temperature, (which would be the sum of temperatures divided by 30).

(1) In City X last April, the sum of the 30 daily high temperatures was 2,160° --> gives the average temperature, but not info about the median. Not sufficient.

(2) In City X last April, 60 percent of the daily high temperatures were less than the average daily high temperature --> each temperature (term) from the 18 lowest ones (from $$t_1$$ to $$t_{18}$$) given to be less than average, hence the median (average of 15th and 16th terms) would also be less than the average. Sufficient.

Hope it helps.
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Re: In City X last April, was the average (arithmetic mean) [#permalink]  20 Jul 2012, 21:16
1) Is it safe to assume that if more than 50% of the terms within a set are BELOW the mean, then the mean is GREATER than the median?

2) Is it safe to assume that if more than 50% of the terms within a set are ABOVE the mean, then the mean is LESS than the median?
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Re: In City X last April, was the average (arithmetic mean) [#permalink]  20 Jul 2012, 23:40
monirjewel wrote:
1) Is it safe to assume that if more than 50% of the terms within a set are BELOW the mean, then the mean is GREATER than the median?

2) Is it safe to assume that if more than 50% of the terms within a set are ABOVE the mean, then the mean is LESS than the median?

The answer is Yes, to both questions.
The definition of the median is in fact the 50th percentile of the data sample.
The Median is "exactly" in the middle, so 50% of the data are below, and the other 50% are above.
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Re: In City X last April, was the average (arithmetic mean)   [#permalink] 20 Jul 2012, 23:40
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