Median
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ISEE Upper Level Quantitative Reasoning › Median
Use the following data set to answer the question:
Find the median.
Explanation
To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.
So, given the data set
we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get
Now, we will locate the number in the center of the data set.
We can see that it is 6.
Therefore, the median of the data set is 6.
Find the median of the following data set:
Explanation
Find the median of the following data set:
To find the median, first put the numbers in increasing order
Now, identify the median by choosing the middle term
In this case, it is 44, because 44 is in the middle of all our terms.
Find the median of the following data set:
Explanation
Find the median of the following data set:
To find the median, first put the numbers in increasing order
Now, identify the median by choosing the middle term
In this case, it is 44, because 44 is in the middle of all our terms.
Use the following data set to answer the question:
Find the median.
Explanation
To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.
So, given the data set
we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get
Now, we will locate the number in the center of the data set.
We can see that it is 6.
Therefore, the median of the data set is 6.
Consider the data set
.
For what value(s) of would this set have median
?
Any number greater than or equal to
Any number greater than
Any number less than or equal to
Any number less than
Any number except
Explanation
Arrange the eight known values from least to greatest.
For to be the median of the nine elements, it muct be the fifth-greatest, This happens if
.
Consider the data set
.
For what value(s) of would this set have median
?
Any number greater than or equal to
Any number greater than
Any number less than or equal to
Any number less than
Any number except
Explanation
Arrange the eight known values from least to greatest.
For to be the median of the nine elements, it muct be the fifth-greatest, This happens if
.
What is the median of the frequency distribution shown in the table:
Explanation
There are data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the
and
largest values. So we can write:
So:
Find the median of the following numbers:
Explanation
The median is the center number when the data points are listed in ascending or descending order. To find the median, reorder the values in numerical order:
In this problem, the middle number, or median, is the third number, which is
If is a real number, find the median in the following set of data in terms of
.
Explanation
The data should first be ordered:
When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the and
values:
What is the median of the frequency distribution shown in the table:
Explanation
There are data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the
and
largest values. So we can write:
So: