# How to Find the Median for Group Data

The **median of a group of data** refers to the middle-most figure in the group. It also refers to the figure that is halfway in the set. You would need to arrange your data from smallest to largest in order to find the median. Unlike a list of data, grouped data does not have individual values and calculating their sum is not possible. So, you will have to determine the middle point of the data to calculate its median.

The Median would be the sum of products divided by the number of values in total. Read this oneHOWTO article to find out in detail **how to find the median for group data**.

## What is the median in mathematics?

In terms of mathematics, there are **three different kinds of averages**: the mode, mean and median. Each of them has a particular normal value. **Mode** refers to the most common value appearing in data, while mean is the value that you get when you share the data in equal portions, and median is what appears in the middle of the data. Let’s expand:

**Mode**: Mode refers to the number that is the most visible and appears the most in a group of numbers.

**Mean**: Mean refers to the value you get when you add up all the numbers in a group and then divide the sum by the number of figures in the list, i,e:** the average**. You can easily calculate the mean if all the numbers are grouped together and equally distributed.

**Median**:The median however, is the number which you find in the middle of a list.

You may use different types of averages in particular situations, based on what you are communicating with the sum.

## Step by Step Instructions

**Steps to Find the Median: **

In order to find the **median**, follow these instructions:

- First of all, arrange all the numbers of the group in order. If the numbers are not placed in order, you need to sort them out. You may arrange in either ascending or descending order.
- Then find the figure that is situated in the middle. To do that, start circling one number at both ends of the list. While doing this, you will be encircling two numbers at a time, one at each end of the list. Keep circling until only one or two numbers are left in the middle.
- If only one figure is left in the middle, that figure is your median and you don’t need to do anything else.
- If two numbers are left in the middle, then you will need to find the
**mean**. You can do this by adding up both the numbers and then dividing them by a sum of two. The answer is your median.

**Steps to Find the Mode:**

If the figures in your list are placed in order, then try to find out which number appears most often. Count the frequency of the value and find out which figure appears the most. For instance, if these are the following numbers in your list: 1, 2, 3, 3, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10.

The number 9 appears more frequently than other numbers, so the mode of this data is 9. If the data is not provided in the list, you can make a tally chart to count the numbers and find the mode.

**Steps to Find the Mean**

In order to find the mean, follow these instructions:

- Make a list of all the numbers that appear in the data.
- Add all these numbers and find the sum.
- Count the number of numbers which appear in the list.
- Divide the sum you found earlier by the total number of numbers in the list.
- The answer that you get is the
**mean**of your data. You will find that the mean is somewhere in the middle of the lowest and highest numbers of your list.

**Example of finding mean: **

- 1+ 7+ 8+ 5 +8
- = 29.
- 29 / 5 (numbers in the list)
**median**= 5.8

## Things to consider while calculating median

Here are a few things that you need to keep in mind when **finding the median for group data**:

- Will you use the median only for measuring central tendency, or you are going to apply it to other data representations as well?
- If you are going to apply it to other data representations, then is it possible to calculate or estimate the value from this presentation?
- Are there any other measures that you can use to find this median, in case finding it not the best thing to do?

## Tips in finding the median of group data

In terms of statistics, median and average are the two varied representations of a data set’s middle point. It may give stories about data that are very different from each other, especially if there are outliers in the data set.

The mean is the most frequently used by statisticians to find the **middle of a data set containing numbers**. Mean is the total of all values in a group of data divided by the number of figures in the group. For instance, if you are calculating the mean (average) of population of a city, the mean is termed as the population mean. Remember, sometimes, mean does not give a fair representation of data, probably because it can be easily affected by outliers.

**Median** is a way to measure the middle point of a group of numbers. On many American highways, the middle lane is called as median, and it has equal number of lanes on both sides of it. In a group of numbers, median is the value which has an equal number of entries above and below it. Simply put, median is the middle point of a group of data.

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