Median Calculation Explained

To find the median of a set of numbers, we need to follow a specific process. The median represents the middle value when the numbers are arranged in order. Let's break down the steps to calculate the median for the given set: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138.

Step 1: Sort the Numbers

First, arrange the numbers in ascending order (from smallest to largest):

130, 137, 138, 138, 144, 146, 149, 154, 156, 160

Step 2: Count the Numbers

Count how many numbers are in the set. In this case, there are 10 numbers.

Let n be the total count of numbers. So, n = 10.

Step 3: Identify the Middle Value(s)

Since there is an even number of data points (n = 10), the median is the average of the two middle numbers. The positions of these middle numbers can be found using the formulas:

• Position 1: n / 2
• Position 2: (n / 2) + 1

Applying this to our set:

• Position 1: 10 / 2 = 5^th position
• Position 2: (10 / 2) + 1 = 5 + 1 = 6^th position

Now, find the numbers at these positions in the sorted list:

• The number at the 5^th position is 144.
• The number at the 6^th position is 146.

Step 4: Calculate the Median

To find the median, calculate the average of the two middle numbers identified in the previous step.

Median = $\frac{\text{Value at } n/2 \text{ position} + \text{Value at } (n/2) + 1 \text{ position}}{2}$

Median = $\frac{144 + 146}{2}$

Median = $\frac{290}{2}$

Median = 145

Therefore, the median of the given set of numbers is 145.