ISEE Middle Level Quantitative : Data Analysis and Probability
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #1 : Median
Which is the greater quantity?
(A) The median of the data set
(B) The median of the data set
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
(A) and (B) are equal
(A) and (B) are equal
Each data set has five elements; the median is the element in the middle after the elements are arranged in ascending sequence, which both are. In each case, the median will be the third-highest element. Since in both data sets, this element is 100, the medians are equal.
Example Question #3 : How To Find Median
Give the median of the data set
The median of a data set with an even number of elements is the mean of the two elements in the middle when they are arranged in ascending order. The data set has six elements, so the median is the mean of the third-highest and third-lowest elements:
Example Question #3 : How To Find Median
The median of the weights of the nine students in the history club is 150 pounds. What is the sum of their weights?
(A) 1,350 pounds
(B) The sum of the weights of the students
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
It is impossible to determine which is greater from the information given
It is impossible to tell which is greater.
For example, if all nine students weight 150 pounds, their median weight is 150, and their total weight is equal 
If, however, their weights are
then the median of their weights - the middle value - is still 150 pounds, but the sum of their weights is
Example Question #111 : Data Analysis And Probability
Consider the data set
Which of the following elements replaces the box to make 50 the median of the data set?
None of the other responses are correct.
None of the other responses are correct.
The median of eleven elements is the element in the middle when arranged in ascending order - that is, the sixth-lowest element. If the box is replaced with a 40, the data set becomes
making 40 the sixth element.
If the box is replaced with a value less than 40, then the lowest five values are 20, 30, 30, 40, and the new element, and the sixth element is 40.
If the box is replaced with a value greater than 40, then the lowest five values are 20, 30, 30, 40, 40, and the sixth element is 40.
No matter what, the median is 40.
Example Question #5 : How To Find Median
The six students in the science club weigh 145 pounds, 172 pounds, 166 pounds, 159 pounds, 153 pounds, and 201 pounds. Give the median of their weights.
In ascending order, their weights are:
The median is the average of the two numbers in the middle of the set, which are 159 and 166:
The median weight is 162.5 pounds.
Example Question #2 : Median
Consider the data set 
Which of the following elements, when plugged in for the square, make 40 the median of the data set?
All of the other responses are correct.
All of the other responses are correct.
The median of eleven elements is the element in the middle, assuming the numbers are arranged in order.
If the box is replaced with a 40, the data set becomes
making 40 the sixth element.
If the box is replaced with a value less than 40, then the lowest five values are 20, 30, 30, 40, and the median is 40.
If the box is replaced with a value greater than 40, then the lowest five values are 20, 30, 30, 40, 40, and the median is 40.
No matter what, the median is 40.
Example Question #1 : Median
The six students in the science club weigh 
In ascending order, their weights are:
The median is the average of the two numbers in the middle of the set, which are 
The median weight is 
Example Question #3 : Median
Give the median of the following eight scores:
Arrange the scores from least to greatest.
There are an even number (eight) of scores, so the median is the arithmetic mean of the middle two scores, 72 and 73. This makes the median
Example Question #4 : Median
Find the median of this set of numbers:
753, 159, 456, 654, 852, 963, 741.
First, order the numbers from least to greatest.
Then, identify the middle number:
Example Question #1 : Find Median
Find the median of this set of numbers:
60, 74, 51, 43, 91,62, 65
First, place the numbers in order from least to greatest:
Then, identify the middle number: 62.
All ISEE Middle Level Quantitative Resources
