GRE Math : How to find arithmetic mean
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Example Questions
Example Question #27 : Statistics
Lucy averages 83% on her first 5 tests. What must she score on her sixth test to raise her class average to an 84, assuming all tests are weighted equally?
89
91
85
84
90
89
For the first 5 tests, Sum / 5 = 83, so Sum = 5 * 83 = 415.
Now to solve for the last test, (415 + x) / 6 = 84. Then 415 + x = 504, and x = 89.
Example Question #112 : Data Analysis
There exists a function f(x) = 3x + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?
6
4
20
25
14
14
First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:
average = (8 + 11 + 14 + 17 + 20) / 5 = 14
Example Question #21 : How To Find Arithmetic Mean
What is the arithmetic mean (average) of the following set of numbers:
34, 26, 18, 12, 40
18
34
40
12
26
26
If in a set of numbers, the numbers are: 
To find the average, add up the sum of all the numbers and divide by the number of items present.
Example Question #22 : How To Find Arithmetic Mean
What is the average (arithmetic mean) of all multiples of five from 5 to 45 inclusive?
25
15
24.4
28
20
25
All multiples of 5 must first be added.
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 = 225
Because we added 9 terms, the product must be divided by 9.
225 / 9 = 25.
25 is the average.
Example Question #23 : How To Find Arithmetic Mean
What is the average of 
Average is the sum of all the terms divided by the number of terms. So:
Example Question #24 : How To Find Arithmetic Mean
If the average test score of three students is 70, which of the following could a fourth student receive such that the average of all four scores is greater than 73 and less than 75?
The sum of the scores of the first three students whose average was 70 is 
If the average needs to be between 73 and 75 then:
Solving for
Only 83 falls in that range.
Example Question #115 : Data Analysis
Jane had an arithmetic mean of 84 on the first four math tests she took this year. By the time she'd taken six tests, her arithmetic mean was 86. Assuming that 100 is the maximum number of points possible per test, what is the lowest score that Jane could have possibly received on her fifth test?
To achieve an average of 84 on the first four tests, Jane would have to have received a total of 
Example Question #21 : How To Find Arithmetic Mean
Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.
which sequence is correct for the number set: 8, 3, 11, 12, 3, 4, 6, 15, 1 ?
The answer is 
First organize the number set 1, 3, 3, 4, 6, 8, 11, 12, 15
a = range = 14
b = mean = 7
c = median = 6
d = mode = 3
so the order is mode<median<mean<range
or d < c < b < a.
Example Question #25 : How To Find Arithmetic Mean
Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.
Which sequence is correct for the number set: 51, 8, 51, 17, 102, 31, 20
c < a < d < b
a < b < d < c
d < c < a < b
c < b < d < a
b < d < c < a
c < b < d < a
The answer is c < b < d < a.
When we arrange the number set we see: 8, 17, 20, 31, 51, 51, 102
a = range = 94
b = mean = 40
c = median = 31
d = mode = 51
median < mean < mode < range so c < b < d < a
Example Question #26 : How To Find Arithmetic Mean
Jim got scores of 84, 78, 92, and 89 on the first four exams in his math class. What must he get on the fifth exam to have an average score of 88 for all five exams?
91
99
97
95
93
97
Write out the average formula, with x representing the fifth score, and filling in 88 as the average score we want.
Then isolate and solve for x.
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