**Median:**

The median is a measure of central tendency in statistics. It is the middle value in a given set of data when arranged in ascending or descending order. In other words, it is the value that separates the data into two equal halves.

**Calculating the Median:**

To find the median, follow these steps:

1. Arrange the data in ascending or descending order.
2. If the number of data points is odd, the median is the middle value.
3. If the number of data points is even, the median is the average of the two middle values.

**Example:**

Let's consider the following set of data:
5, 8, 10, 12, 15, 16, 18

1. Arrange the data in ascending order:
5, 8, 10, 12, 15, 16, 18

2. Since there are 7 data points (an odd number), the median is the middle value, which is 12.

Therefore, the median of the given data set is 12.

**Significance of Median:**

The median is useful when dealing with skewed data or when outliers are present. Unlike the mean, which can be greatly influenced by extreme values, the median is more resistant to outliers. It provides a better representation of the "typical" value in a data set.

For example, if we have a data set representing the salaries of employees in a company, and there are a few exceptionally high salaries, the mean may be significantly higher due to those outliers. In this case, the median would be a more appropriate measure to understand the central tendency of the salaries.

**Summary:**

- The median is the middle value in a data set when arranged in ascending or descending order.
- It separates the data into two equal halves.
- If the number of data points is odd, the median is the middle value.
- If the number of data points is even, the median is the average of the two middle values.
- The median is useful for skewed data or when outliers are present, as it is less affected by extreme values compared to the mean.

☑ The Median is the "middle" of a sorted list of numbers.

↪ How to Find the Median Value ?

✅ To find the Median, place the numbers in value order and find the middle.

Example: find the Median of 12, 3 and 5

Put them in order:

3, 5, 12

The middle is 5, so the median is 5.


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Example: 

✏ 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

 When we put those numbers in order we have:

✏ 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

 
✅ There are fifteen numbers. Our middle is the eighth number:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

🌟 The median value of this set of numbers is 23 🌟

 
👍(It doesn't matter that some numbers are the same in the list.)👍

💫Two Numbers in the Middle💫

BUT, with an even amount of numbers things are slightly different.

In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two.

Example:

✏3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29

 When we put those numbers in order we have:

✏3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

 
➡There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

 ✅In this example the middle numbers are 21 and 23.

✔ To find the value halfway between them, add them together and divide by 2:

21 + 23 = 44
🌟 then 44 ÷ 2 = 22 🌟

 So, the Median in this example is 22.

 
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)



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