Median - ISEE Middle Level Quantitative Reasoning
Card 0 of 665
Find the median of this set of numbers:
753, 159, 456, 654, 852, 963, 741.
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: 
First, order the numbers from least to greatest.
Then, identify the middle number:
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Find the median of this set of numbers:
60, 74, 51, 43, 91,62, 65
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.
First, place the numbers in order from least to greatest:
Then, identify the middle number: 62.
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Give the median of the following eight scores:
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
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
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Give the median of the following nine scores:
Give the median of the following nine scores:
Arrange the scores from least to greatest.
There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.
Arrange the scores from least to greatest.
There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.
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What is the median of the following set of numbers:
What is the median of the following set of numbers:
The median is the number with an equal number of other items both above and below it. There are 9 total numbers in the list, 4 of them are below 7, and 4 of them are above 7.
The median is the number with an equal number of other items both above and below it. There are 9 total numbers in the list, 4 of them are below 7, and 4 of them are above 7.
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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 median distance that Brandon runs?
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 median distance that Brandon runs?
In order to find the median, we must first put the data in numerical order from least to greatest:
Next, we must find the number that is in the middle, but since there are fourteen numbers, there is no number that falls exactly in the center. When this happens, we add the two middle numbers together and divide by two. In this case, our middle numbers are 
and 
.
Brandon's median distance is 
.
In order to find the median, we must first put the data in numerical order from least to greatest:
Next, we must find the number that is in the middle, but since there are fourteen numbers, there is no number that falls exactly in the center. When this happens, we add the two middle numbers together and divide by two. In this case, our middle numbers are
Brandon's median distance is
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What is the median of the values 
, 
, 
, 
, 
?
What is the median of the values
The median of a set of values is the value that is in the middle when you rearrange the values from least to greatest. In this set, the values can be rearranged as 
, 
, 
, 
, 
and the median is 
.
The median of a set of values is the value that is in the middle when you rearrange the values from least to greatest. In this set, the values can be rearranged as
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On a math test that the teacher gave her students, the scores were as follows:
What was the median score?
On a math test that the teacher gave her students, the scores were as follows:
What was the median score?
The median is the middle number in a set when the set of numbers is ordered sequentially.
When the intial set is reordered sequentially, you get the bottom set. (The top set is the original ordering of the numbers.)
In this sequential set of 7 numbers, the number 89 is in the fourth posiiton and exactly in the middle. Therefore, it is the mean.
The median is the middle number in a set when the set of numbers is ordered sequentially.
When the intial set is reordered sequentially, you get the bottom set. (The top set is the original ordering of the numbers.)
In this sequential set of 7 numbers, the number 89 is in the fourth posiiton and exactly in the middle. Therefore, it is the mean.
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Which is the greater quantity?
(A) The median of the data set 
(B) The median of the data set 
Which is the greater quantity?
(A) The median of the data set
(B) The median of the data set
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.
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.
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Give the median of the data set 
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:
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:
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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.
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.
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.
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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
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
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 
pounds.
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
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
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What is the median of this set of numbers?
What is the median of this set of numbers?
To find the median of a set of numbers, you must first reorder them from smallest to largest. Below is the set reordered as such:
The median is the middle number of the set. Here, 57 is the middle number. Therefore, it is the median and the correct answer.
To find the median of a set of numbers, you must first reorder them from smallest to largest. Below is the set reordered as such:
The median is the middle number of the set. Here, 57 is the middle number. Therefore, it is the median and the correct answer.
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Consider the data set 
.
Which of the following elements, when plugged in for the square, make 40 the median of the data set?
Consider the data set
Which of the following elements, when plugged in for the square, make 40 the median of the data set?
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.
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.
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Consider the data set
Which of the following elements replaces the box to make 50 the median of the data set?
Consider the data set
Which of the following elements replaces the box to make 50 the median of the data set?
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.
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.
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Horatio's soccer team has scored the below number of goals in their last eight games, what is the median number of goals that have been scored?
Horatio's soccer team has scored the below number of goals in their last eight games, what is the median number of goals that have been scored?
First we must put the numbers 
in order from least to greatest.
After the numbers are in order, if it is an odd number of numbers we chose the middle number - that is the median.
In this case, we have an even number of numbers, so we must take the average of the middle two numbers which is given below:
So the median is 
!
First we must put the numbers
After the numbers are in order, if it is an odd number of numbers we chose the middle number - that is the median.
In this case, we have an even number of numbers, so we must take the average of the middle two numbers which is given below:
So the median is
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Horatio's soccer team has scored the below number of goals in their last 
games:
Horatio calculates the median to be 
for this set of data. He then goes back and finds that the game where he thought they scored 9 goals; his team actually scored 
goals - how will this change the median if he replaces the 
with 
in the data set?
Horatio's soccer team has scored the below number of goals in their last
Horatio calculates the median to be
When finding the median we must first reorganize the numbers from least to greatest, here is what the numbers are before and after they were organized.
Given: 
After Organized from least to greatest: 
In order to find the Median for an even number of numbers (we have 
numbers in this set) we take the average of the middle two numbers.
Here we would add 
which is 
, we then divide by two to find the mean which is 
.
If we were to change the 
to an 
, this does not impact the middle two numbers, they will remain 
and 
which means the Median will remain 
.
The middle two numbers are still 
and 
.
The Median will remain unchanged.
When finding the median we must first reorganize the numbers from least to greatest, here is what the numbers are before and after they were organized.
Given:
After Organized from least to greatest:
In order to find the Median for an even number of numbers (we have
Here we would add
If we were to change the
The middle two numbers are still
The Median will remain unchanged.
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Given the following data sets of data, identify how the median would change if an additional data point of 
was added to the new set?
Data Set: 
New Data Set: 
Given the following data sets of data, identify how the median would change if an additional data point of
Data Set:
New Data Set:
First, we need to find the median for the first data set:
We must put the numbers in order from least to greatest:
Since there is an even number of items in the data set, we will take the average of the middle two numbers to find the median.
The median for this data set is:
Next, we must find the new median for the new data set:
Again, we must put the numbers in order from least to greatest:
Since there is an odd number of items, we can choose the middle number to be the median.
In this case, the middle number is 
, which means the new median is:
Therefore, we know that the median will decrease by 
.
First, we need to find the median for the first data set:
We must put the numbers in order from least to greatest:
Since there is an even number of items in the data set, we will take the average of the middle two numbers to find the median.
The median for this data set is:
Next, we must find the new median for the new data set:
Again, we must put the numbers in order from least to greatest:
Since there is an odd number of items, we can choose the middle number to be the median.
In this case, the middle number is
Therefore, we know that the median will decrease by
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Find the median of the data set provided:
Find the median of the data set provided:
In order to answer this question correctly, we need to recall the definition of median:
Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.
In order to find the median, we need to first organize the data from least to greatest:
Next, we can solve for the median by finding the middlemost number in our data:
The median for this data set is 
In order to answer this question correctly, we need to recall the definition of median:
Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.
In order to find the median, we need to first organize the data from least to greatest:
Next, we can solve for the median by finding the middlemost number in our data:
The median for this data set is
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Find the median of the data set provided:
Find the median of the data set provided:
In order to answer this question correctly, we need to recall the definition of median:
Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.
In order to find the median, we need to first organize the data from least to greatest:
Next, we can solve for the median by finding the middlemost number in our data:
The median for this data set is 
In order to answer this question correctly, we need to recall the definition of median:
Median: The median of a data set is the middle value, when the data set is ordered from least to greatest.
In order to find the median, we need to first organize the data from least to greatest:
Next, we can solve for the median by finding the middlemost number in our data:
The median for this data set is
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