Averages
Of all statistical topics, averages are tested most frequently. Unfortunately, most
average questions will not be as simple as the preceding one. Usually, the GRE will
give you the average for a set and expect you to solve for the values of one or more
data points in a set or the number of items in a set. Regardless of how the question
is framed, you will always use the average formula: A = NS.If the word “average” appears on the GRE, it will always be followed by
“(arithmetic mean).” For example, a question might ask: “What is the
average (arithmetic mean) of 6 and 8?” Don’t be swayed by the term
arithmetic mean—it’s just a fancy term for average.If a company’s average yearly revenue over a 10-year period was $550,000,
what was the company’s total revenue during that period?SOLUTION: Since you want to solve for the sum, manipulate the average
formula to isolate the sum:
A = NS
A × N = S
Substitute the given values for A and N: 550,000 × 10 = $5,500,000.
Sometimes you will have to use the average formula multiple times in a question:The average height of eight students is 64 inches. If the average height of
seven of the students is 62, how tall is the eighth student?SOLUTION: Use the average formula to determine the sum of the heights of all
eight students:
A × N = S
64 × 8 = 512
Next, use the average formula to determine the sum of the heights of seven of
the students:
A × N = S
62 × 7 = 434
Let the height of the eighth student = h. You know that h + (the sum of the
heights of the seven other students) = (the sum of the heights of the eight
students). Thus h + 432 = 512 → h = 80.
An even more difficult example will use three averages in the question:
A company’s average daily revenue over a 10-day period was $40,000. If the
average daily revenue for the first 4 days was $25,000, what was the average
daily revenue for the last 6 days?328 PART 4 ■ MATH REVIEW04-GRE-Test-2018_313-462.indd 328 12/05/17 12:03 pm