DS-2

What is the average (aritmetic mean) hight of the n people in a certain group?

1 the average hight of the n/3 talles people in the group is 6 feet and 2 1/2 inches and the average height of rest of the people in the group is 5 feet and 10 inches.

2 The sum of the lenghts of the people is 178 feet and 9 inches.



Looking at statement (2) first, we see that it is not sufficient, because the average (arithmetic mean) of a group of numbers is defined as (sum of data) / (# of data points). With statement (2), we only have the numerator of this expression (the # of people in the group is unknown), so we can't figure out the average.

Looking at statement (1) alone, we can set up the average as follows:
Average = (sum of data points) / (# of data points)
= [(n/3)(74.5) + (2n/3)(70)] / (n) <-- note that I used inches here, so I won't have to write in more fractions than necessary (trying to write fractions on this forum is not fun) = [(1/3)(74.5) + (2/3)(70)] / (n) There's no need to simplify further, because the 'n' is gone: you get one number. Therefore, this statement is sufficient. Answer = A Note that, if you have the averages of all the FRACTIONS or PERCENTAGES of a group, then you'll be able to calculate the overall average of the group. This is a worthwhile fact to memorize for the data sufficiency problems