ISEE Upper Level Quantitative : How to find median
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Example Questions
Example Question #573 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
A data set has six known quantities and two unknown positive quantities, as follows:
It is known, however, that
Which is the greater quantity?
(A) The mean of the data set
(B) The median of the data set
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
It is impossible to determine which is greater from the information given
If 
The median of the data set, however, depends on the values of 
Case 1:
The data set is then
and the median is the mean of the two middle values. Since both middle values are 35, the median is 35.
Case 2: 
The data set is then
and the median is the mean of the two middle values. They are 25 and 35, so the median is
In the first case, the median is greater than the mean; in the second case, the mean is greater than the median. Therefore, the information is insufficient.
Example Question #581 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
A data set has six known quantities and two unknown quantities, as follows:
Which is the greater quantity?
(A) The median of the set if 
(B) The median of the set if 
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) and (B) are equal
The median of a data set with an even number of elements is the mean of the middle two numbers, assuming the elements are arranged in order; since the data set has eight elements, the median will be the mean of the fourth-lowest element and the fourth-highest element.
If 
Note: You don't need to do the last step and actually find the median. As long as you know that the two medians are the same, you've answered the question!
Example Question #582 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Over each of the past seven days, Beth has driven the following number of miles:
If M is equal to the mode, N is equal to the median, and O is equal to the mean, what is the order of M, N, and O from smallest to largest?
The first step is to reorder the set, 
The mode (which occurs most often) is 3.3, so 
The median is the middle number in the set (which is 6.8, having 3 numbers to its right and 3 to its left in the ordered list), so 
The mean (or average) is 
Therefore, 
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