ISEE Upper Level Quantitative : Data Analysis and Probability
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #101 : Data Analysis And Probability
Mark's numeric grade in his Spanish class is determined by five equally weighted hourly tests and a final, weighted twice as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Mark's hourly test scores are 92, 66, 84, 77, and 87. What must Mark score on his final, at minimum, in order to achieve a grade of 80 or better for the term?
Mark's grade is a weighted mean in which his hourly tests have weight 1 and his final has weight 2. If we call 
which simplifies to
Since Mark wants his score to be 80 or better, we solve this inequality:
Mark must score 77 or better on his final.
Example Question #5 : How To Find Mean
A gymnastics contest has seven judges, each of whom rates each contestant's performance on a scale from 0 to 10. A contestant's score is calculated by disregarding the highest and lowest scores, and taking the mean of the remaining five scores.
The seven judges rated Sally's performance with the following seven scores: 
Which of these quantities is the greater?
(a) Sally's score
(b) Sue's score
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It cannot be determined from the information given.
(b) is greater.
To calculate whether Sally or Sue has the higher average, it is only necessary to add, for each contestant, all of their scores except for their highest and lowest. Since both sums are divided by 5, the higher sum will result in the higher mean score.
(a) For Sally, the highest and lowest scores are 9.7 and 9.1. The sum of the other five scores is:
(b) For Sue, the highest and lowest scores are 10.0 and 9.1. The sum of the other five scores is:
Sue's total - and, subsequently, her score - is higher than Sally's, so (b) is the greater quantity.
Example Question #102 : Data Analysis And Probability
A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10; a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.
The seven judges individually assigned the following scores to one of Kathy's routines:
Which is the greater quantity?
(a) Kathy's score for the routine
(b) 9.5
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
(a) is greater.
The highest and lowest scores of the seven are 9.9 and 9.3, so Kathy's score is the mean of the other five:
This makes (a) greater.
Example Question #103 : Data Analysis And Probability
A student's course average is determined by calculating the mean of five tests. Chuck is trying for an average of 
Which is the greater quantity?
(a) The score Chuck needs on the fifth test to achieve his goal
(b)
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
(a) is greater.
For Chuck to achieve an average of 
Example Question #104 : Data Analysis And Probability
Which is the greater quantity?
(a) The mean of the data set
(b)
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(b) is greater
(a) is greater
The sum of the elements in the data set 
Divide by 5 to get the mean:
Example Question #9 : How To Find Mean
Which is the greater quantity?
(a) The mean of the data set:
(b)
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(a) and (b) are equal.
(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 #105 : Data Analysis And Probability
Which is the greater quantity?
(a) The mean of the data set:
(b)
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(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 #106 : Data Analysis And Probability
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.
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(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.
All ISEE Upper Level Quantitative Resources
