Finding the Median of Data

The question asks for the median of a given set of numbers. The median is the middle value in a dataset that has been arranged in order. If there is an even number of data points, the median is the average of the two middle values.

Steps to Calculate the Median

To find the median, follow these steps:

• Arrange the data in ascending order (from smallest to largest).
• Count the total number of data points (let this be '$n$').
• Determine if '$n$' is odd or even.
  • If '$n$' is odd, the median is the middle value. The position of the median is given by the formula: $ \frac{(n + 1)}{2} $.
  • If '$n$' is even, the median is the average of the two middle values. The positions of these two values are $ \frac{n}{2} $ and $ \frac{n}{2} + 1 $.

Applying the Steps to the Given Data

The provided data set is: 24, 30, 40, 80, 15, 57, 78, 82, 39, 97, 82.

1. Order the Data

First, let's arrange the numbers in ascending order:

2. Count the Data Points

Let's count how many numbers are in the list. There are 11 data points. So, $n = 11$.

3. Determine the Median Position

Since $n = 11$, which is an odd number, we use the formula for the odd case to find the position of the median: $ \text{Position} = \frac{(n + 1)}{2} $ $ \text{Position} = \frac{(11 + 1)}{2} $ $ \text{Position} = \frac{12}{2} $ $ \text{Position} = 6 $

This means the median is the 6th value in the ordered list.

4. Identify the Median Value

Looking at the ordered list (15, 24, 30, 39, 40, 57, 78, 80, 82, 82, 97), the 6th value is 57.

Therefore, the median of the given data is 57.