Problem Solving

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

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.

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

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?

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.