ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #7 : How To Find Mean
Which is the greater quantity?
(a) The mean of the data set:
(b)
(a) and (b) are equal.
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
The sum of the elements in the data set 
Divide by 5 to get the mean:
(b)
(b) is greater.
Example Question #5 : Mean
Which is the greater quantity?
(a) The mean of the data set:
(b)
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
(a) and (b) are equal.
(b) is greater.
(a) The mean of the data set is the sum of its elements divided by 
(b)
(b) is greater.
Example Question #102 : Data Analysis
John's grade in his economics class is the mean of his best five test scores out of the six tests he takes.
John's first five test scores are:
Which is the greater quantity?
(a) The lowest score John must take to achieve a score of at least a score of 
(b)
It is impossible to tell from the information given.
(a) is greater.
(a) and (b) are equal.
(b) is greater.
(b) is greater.
John's current point sum is 
Even if John achieves a score lower than 
Example Question #103 : Data Analysis
A student's grade in Professor Jackson's Shakespeare class is the mean of his or her four best test scores out of five.
Craig and his brother Jerry have been in a friendly competition to see who can get the best grade in the class.
Craig outscored Jerry on the first test by 9 points and on the fifth test by 5 points. Jerry outscored Craig by 6 points on the second test and by 8 points on the fourth. Their scores were identical on the third.
Which is the greater quantity?
(a) Craig's grade
(b) Jerry's grade
It is impossible to tell from the information given.
(a) and (b) are equal.
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
This question cannot be answered.
Let 
We need to compare the sums after the lowest test for each student is disregarded, since each will be divided by the four tests. But it is not known which test will be thrown out for each student.
If, for example, the first test is thrown out for both Craig and Jerry, Craig's total will be
and Jerry's score will be higher.
If the second test is thrown out for both Craig and Jerry, Craig's total will be
and Craig's score will be higher.
Example Question #11 : Mean
A student's grade in Professor Kalton's abstract algebra class is the mean of his or her five test scores.
Philip outscored Kellie on the first test by 8 points and on the second test by 5 points. They scored the same on the third test. Kellie outscored Philip by 7 points on the fourth test and by 6 points on the fifth.
Which is the greater quantity?
(a) Philip's grade
(b) Kellie's grade
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(b) is greater.
(a) and (b) are equal.
You do not need to take the two means; just compare the sums, since each will be divided by 5.
Let 
Philip and Kellie scored the same number of points, making their mean test scores the same.
Example Question #12 : Mean
Katie's grade in her Shakespeare class is the mean of her best five test scores out of six tests taken.
Her test scores are 
Which is the greater quantity?
(a) Katie's grade
(b)
(a) and (b) are equal.
(a) is greater.
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
Take the sum of all of her test scores except for her lowest and divide that by the number of test scores included.
Example Question #13 : Mean
Consider the following set of numbers:
Quantity A: Median of the set
Quantity B: Mean of the set
Quantity A is greater.
The relationship cannot be determined from the information given.
Quantity B is greater.
The two quantities are equal.
Quantity B is greater.
The median of the set of numbers is determined by arranging the numbers in numerical order and finding the middle number. In this case there are two middle numbers, 
The mean is found by dividing the sum of elements by the number of elements in the set:
Quantity B is larger.
Example Question #14 : How To Find Mean
Compare 
The quantity of 
The quantity of 
The two quantities are equal.
It is not possible to determine which quantity is greater.
The quantity of
The average of a list of terms can be found as follows:
So we can write:
So 
Example Question #14 : How To Find Mean
Which one is greater:
It is not possible to tell from the information given
Mean of a data set 
So we have:
So the mean of the first data set is greater.
Example Question #115 : Data Analysis And Probability
Which one is greater:
It is not possible to tell from the information given
Mean of a data set 
So we have:
All ISEE Upper Level Quantitative Resources
