# How Do You Find Median in a Frequency Table?

Median is a central tendency. Here, you will learn how to find the median in a frequency table

The first step towards finding the median in a frequency table is to find the middle value in a data set. The sum of all the frequencies in a frequency table is called $n$. The number $n$ is very important when you want to find the median in a frequency table.

Rule

### TheMiddleNumberinaFrequencyTable

There are two cases:

1.
$n$ is an odd number:
2.
If $n$ is an even number, there are two middle numbers:

Finding the median is easy once you have the middle number.

Rule

### MedianinaFrequencyTable

The median is simply the value of the middle number. If $n$ is an even number, where there are two middle numbers, then the median is the mean of these two numbers.

This will be easier to understand after looking at a couple of examples.

Example 1

This frequency table shows how many PCs a group of youth have in their home.

 Number of PCs Frequency 0 2 1 7 2 6 3 3 4 0 5 1

Find median number of PCs per house.

In order to find the middle number, you need to first know how many homes there are. This is the same as the sum of the frequencies, or how many youth who were asked this question. This sum is

 $2+7+6+3+0+1=19.$

Since 19 is an odd number there is only one number in the middle and we can use the rule above

 $\frac{19+1}{2}=10.$

The tenth person is the median. So who was the tenth person? There were two youth with no PCs. There were seven with one, so that’s $2+7=9$ with one or less. So the tenth person must be the first with 2 PCs. So the median is 2.

You could have seen this more easily by expanding the table with cumulative frequency. Let’s try that!

 Number of PCs Frequency Cumulative Frequency $0$ $2$ $2$ $1$ $7$ $9$ $2$ $6$ $15$ $3$ $3$ $18$ $4$ $0$ $18$ $5$ $1$ $19$

You see that the first row in cumulative frequency to cross 10 is the row with 2 PCs. This is another way of seeing that the median is 2.

What if the sum $n$ is an even number? You will see that case in the next example.

Example 2

You take a walk in a street in Hollywood and count the number of cars per home. You organize the information you find in the frequency table below. Since you remember that having the cumulative frequency can be helpful, you add that right away.

 Number of Cars Frequency Cumulative Frequency $0$ $1$ $1$ $1$ $4$ $5$ $2$ $7$ $12$ $3$ $6$ $18$ $4$ $2$ $20$ $5$ $4$ $24$

Find the median number of cars.

As in Example 1, you need to find the middle number by adding the number of homes together. This is the sum of the frequencies:

 $1+4+7+6+2+4=24.$

You could have also seen this from the last row in the cumulative frequency. Since 24 is an even number, there are now two middle numbers:

 $\frac{24}{2}=12$

and

 $\frac{24+2}{2}=13.$

The 12. and 13. person is the middle number. You can see from the cumulative frequency that the 12. person have two cars and the 13. person is the first to have three cars. The median is the mean of these two:

 $\frac{2+3}{2}=\frac{5}{2}=2.5.$

Median number of cars per house in this street is $2.5$.