These basic statistical terms are extremely important on the GRE.
Strictly speaking, a list and a set have different meanings. The elements in a list are ordered, while the elements in a set can be in any order. On the GRE, these terms are usually interchangeable unless you’re working with probability.
Let’s go through some examples.
The mode is the number that appears most often.
What is the mode of Set A ?
Answer: 4
There are two 4s and only one of each other number. Since 4 occurs most frequently, it’s the mode.
The range is the difference between the maximum and minimum values.
What is the range of Set A ?
Answer: 11
The minimum is 2 and the maximum is 13, so the range is .
The mean is found by adding all the numbers and dividing by the number of elements.
What is the mean of Set A ?
Answer: 3.2
The sum is . There are numbers, so the mean is .
The median is the middle value after you put the numbers in order.
What is the median of Set A ?
Answer: 3
When the numbers are in order, 3 is in the middle. If the list were in a different order, you would still sort it first, and the median would still be 3.
What if you wanted the median of the list ? There isn’t a single middle number. In that case, the median is the mean of the two middle numbers.
The two middle numbers are and , so the median is .
A common question type asks for a new mean after adding a number to a set. Another variation asks what number you must add to reach a target mean. Let’s start with the first variation.
If you scored a mean of 85 points on your first 4 quizzes, what would be the average of all five quizzes if you scored 90 on the final quiz?
First, find the total points from the first 4 quizzes.
Then add the 90 points from the final quiz to get the total for all 5 quizzes.
Now divide by 5 to get the new mean.
So, the average score becomes 86 when you add a fifth quiz score of 90.
Let’s try a slightly different version using the same idea.
You currently have an average score of 97 on your first four quizzes. If you wanted to get an average grade of at least 95 on the five quizzes, what score will you need on the fifth quiz?
Take a moment to see if you can solve it using the technique above.
Answer: 87 or higher
First, find the total points needed for a 95 average across 5 quizzes.
Next, find how many points you already have from the first 4 quizzes.
The score you need on the fifth quiz is the difference.
So the fifth quiz must be at least 87 to make the overall average 95 or higher. You can check this by computing the mean directly:
It checks out.
A weighted average is used when different parts of a total don’t count equally. Instead of treating every value the same, you multiply each value by its weight (a number between 0 and 1), then add the results.
For example, if something is worth 25% of the total, its weight is . The weights for all parts must add up to 1.
A common real-world example is a course grade: the final might be 50% of the grade, attendance 10%, and homework 40%.
When solving for a weighted average, follow these steps.
Try using the steps above to solve this practice problem.
A student just scored an 85 on the final of their economics course. Their average homework score was 82 and they attended 90% of the lectures. What is the student’s final grade if the professor weighs the final at 20% of the grade, attendance at 20%, and homework at 60%?
Are you ready for the answer?
The student’s final grade is
Let’s pull out the key information from the question:
Now write the weighted-average equation and compute.
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