How to find median

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:

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.

The first ten primes form the data set:

(a) Add these primes, and divide by :

(b) The median of a data set with ten elements is the arithmetic mean of the fifth-highest and sixth-highest elements. These are and , so the median is

.

(a) is the greater quantity.

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 .

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:

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:

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

To find the median of a data set, we will first arrange the data set in ascending order. Then, we will find the number that is located in the middle of the set.

So, given the set

we will arrange the set in ascending order (from smallest to largest). We get

Now, we will locate the number in the middle of the set.

We can see that it is 6.

Therefore, the median of the data set is 6.

Each data set has ten elements, so the median in each case is the arithmetic mean of the fifth-highest and sixth-highest elements. In each data set, these elements are 10 and 10, so the median of each set is 10. Therefore, both quantities are equal.

The median of a data set with five elements is its third-greatest element, which here is .