in a city in Hawaii

[sanju09]

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

[2ndShot]

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.

[gmat740]

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

Thank You sanju for pointing my mistake.

I hope my method for quick calculation of a is clear

[sanju09]

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?

[rossmj]

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.