Determine the median value for the following data.23, 17, 41, 12, 14, 40 and 36

1. Break Down the Problem

To find the median of a dataset, you need to follow these steps:

1. Arrange the data in ascending order.
2. Determine the number of data points (n).
3. Calculate the median based on whether n is odd or even.

2. Relevant Concepts

• The median is the middle number in a sorted list of numbers.
• If the number of observations (n) is odd, the median is the middle value.
• If n is even, the median is the average of the two middle numbers.

3. Analysis and Detail

1. Step 1: Arrange the data
   The given data points are: 23, 17, 41, 12, 14, 40, 36

   Arranging them in ascending order:
   12, 14, 17, 23, 36, 40, 41

2. Step 2: Count the number of data points (n)
   The total number of data points (n) is 7, which is odd.

3. Step 3: Find the median
   Since n is odd, the median value is the middle number.
   The middle number in this sorted list is the 4th value.

   Thus, the median is:
   $\text{Median} = 23$

4. Verify and Summarize

We have arranged the data correctly and identified that there are 7 numbers. The 4th number in the sorted list confirms we found the correct median.

Final Answer

The median value for the dataset is 23.