ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #271 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Which is the greater quantity?
(A) The mode of the data set
(B) The median of the data set
(B) is greater
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
Arrange the elements in ascending order.
The mode of the set is the element that appears most frequently, which here is 15.
The median of the set is the element that appears in the middle, which here is 19.
(B) is greater.
Example Question #272 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Which is the greater quantity?
(A) The number of modes of the data set
(B)
(A) is greater
(A) and (B) are equal
(B) is greater
It is impossible to determine which is greater from the information given
(B) is greater
The mode of a data set is the element that appears most frequently. The given data set has no repeated elements; it is considered to have no modes. (B) is greater.
Example Question #273 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Consider the data set
Which of the following elements replaces the box to make 30 the mode of the data set?
None of the other responses is correct.
None of the other responses is correct.
Regardless of what value replaces the box, 40 will still be the most frequently appearing element in the set (four times, more than any other element) - that is, 40 will be the mode.
Example Question #274 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Consider the data set
Which of the following elements replaces the box to make 40 the mode of the data set?
(A)
(B)
(C)
Only (B) is correct.
None of (A), (B), or (C) are correct.
Only (C) is correct.
(A), (B), and (C) are all correct.
Only (A) is correct.
(A), (B), and (C) are all correct.
Regardless of what value replaces the box, 40 will still be the most frequently appearing element in the set (four times, more than any other element). By definition, that makes 40 the mode.
Example Question #275 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Which is the greater quantity?
(A) The number of modes of the data set
(B)
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
Arrange the data set in ascending order.
18 appears three times; 65 and 79 appear two times each; therefore, 18 is the only mode, and (B) is greater.
Example Question #1 : How To Find Mean
Brandon is training for a marathon. Each day after school he runs for two hours. Over the course of two weeks, he runs the following distances:
What is the mean distance Brandon runs in this two week period?
Since the mean is the average of the data, we must calculate the average of Brandon's runs. In order to do this, we first add up all the data points.
Next we divide by the total number of days that Brandon runs, 
We can round this to the nearest tenth, 
Example Question #1 : Mean
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Allie has scored 79, 77, 96, 71, 85, 86, 90, and 84 on her eight science quizzes, and her teacher drops the highest and lowest score.
Column A Column B
Allie's quiz average Allie's quiz average
before the dropped scores after the dropped scores
The quantity in Column A is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
The quantity in Column B is greater.
The two quantities are equal.
Add up the 8 test scores and divide by 8 to figure out the mean (83.5). Now figure out the average between the highest and lowest scores
Since the dropped tests have the same average as the original 8 tests, Allie's score would not change. The correct answer is that the two columns are equal.
Note: If you are good at mental math, here is a quick way to figure out the average of the 8 tests:
First, estimate the average (say, 80). Next, go through the numbers and add or subtract the difference between the number and 80.
79 is 1 below 80.
77 is 3 below 80 (so now we're 4 below 80).
As we continue through the numbers, we get
12 above, 3 above, 8 above, 14 above, 24 above, 28 above.
So the 8 scores are cumulatively 28 above an average score of 80. Now, simply divide 28 by 8 and add this to 80.
Example Question #1 : Mean
A student's grade in Professor Kalton's abstract algebra class is the mean of his or her five test scores.
Kent's five scores are 83, 91, 88, 85, and 80.
Janice's five scores are 87, 87, 84, 85, and 92.
Which is the higher quantity?
(a) Kent's grade
(b) Janice's grade
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
(b) is greater
You do not need to take the two means; just add the scores, since each sum will be divided by 5 to get the students' means.
Kent's total:
Janice's total:
Janice's sum is higher; so is her mean score.
Example Question #2 : Mean
The sum of the weights of the twelve students in the math club is 1,980 pounds. Which is the greater quantity?
(A) The mean of their weights
(B) 175 pounds
(B) is greater
It is impossible to determine which is greater from the information given
(A) is greater
(A) and (B) are equal
(B) is greater
To get the mean of the students' weights, divide the sum of the weights by the number of students; here, this is
(B) is greater.
Example Question #3 : Mean
Consider the data set
Which of the following elements replaces the box to make 42 the mean of the data set?
For the mean of the eleven data elements to be 42, their sum divided by 11 must be 42. Equivalently, the sum of the elements must be 
The sum of the ten known elements is
Therefore, the unknown element must be
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All ISEE Middle Level Quantitative Resources
