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in a city in Hawaii

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by sanju09 » Wed Jul 11, 2012 3:06 am
The table shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?
A. a < m < f
B. a < f < m
C. m < a < f
D. m < f < a
E. a - m < f


Source: collegeboard.org
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by niketdoshi123 » Wed Jul 11, 2012 4:08 am
sanju09 wrote:The table shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?
A. a < m < f
B. a < f < m
C. m < a < f
D. m < f < a
E. a - m < f


Source: collegeboard.org
there are seven days in a week, so the 4th largest will be the median.
m (median temp.) = 75
f (temp. that occurred the most) = 78 ( 2 times)

check the options
the avg cannot be greater than 78
so "f" will be greatest . Eliminate options B & D

By observing the table we can conclude that the mean < 75(median) [applying weighted average property]. that eliminates option C & E,
leaving us with only one option A that is correct.
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