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in a city in Hawaii

by sanju09 » Sat Apr 04, 2009 5:10 am
NOONTIME TEMPERATURES IN HILO, HAWAII

Mon Tue Wed Thu Fri Sat Sun
66 78 75 69 78 77 70

The table above 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
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by 2ndShot » Sun Apr 05, 2009 1:59 am
We can calculate the values for m, f and a from the table given:

m=75, f=78 and a= 513/7 < 75

therefore (A) a<m<f.
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by gmat740 » Sun Apr 05, 2009 5:18 am
Arrange the data in increasing order

66,69,70,75,77,78,78

clearly , m = 75 and f= 78

now how to find average quickly

consider 66 as base value to be 0,now arrange the data

0,3,4,9,11,12,12

a1 = 51/7 = 7.28

since we assumed 66 to be base value and subtracted 66 from each value to simplify calculations

we again add 66 to a = 73.28

so answer is A

a<m<f

I made a silly calculation mistake and so I have edited it, I guess if I make the same mistakes in MY TEST day what is going to happen to my score :shock:

Thank You sanju for pointing my mistake.

I hope my method for quick calculation of a is clear
Last edited by gmat740 on Mon Apr 06, 2009 5:14 am, edited 1 time in total.
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by sanju09 » Mon Apr 06, 2009 2:31 am
0,3,4,9,11,12,12

a = 31/7 == 4.4
but I think that 0 + 3 + 4 + 9 + 11 + 12 + 12 = 51, though it won't effect the conclusion, but should not we be careful? :)
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by rossmj » Mon Apr 20, 2009 10:57 am
M and F are easy enough to figure out, the easiest way to look at the avg is to look at the distance of each value from the median. If the sum is 0 then M=A, if it is negative then A<M, and if it is positive M<A.
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