Find the median of the following six numbers: 14, 12, 12, 16, 13 and 18.

Introduction / Context:
This question focuses on the concept of the median of a data set. Unlike the mean, which is based on total and count, the median is the middle value when the data is arranged in ascending or descending order. For an even number of observations, the median is the average of the two middle values.

Given Data / Assumptions:
- The six numbers are: 14, 12, 12, 16, 13 and 18. - We are asked to find the median of this data set. - Median requires arranging the numbers in ascending order first.

Concept / Approach:
The median is defined as the middle value of an ordered data set. When there is an odd number of values, it is simply the central value. When there is an even number of values, the median is the average of the two central values after sorting. Here we have six values, so we will arrange them, identify the third and fourth values, and compute their average.

Step-by-Step Solution:
Step 1: List the numbers given: 14, 12, 12, 16, 13, 18. Step 2: Arrange them in ascending order. Step 3: Ordered list becomes: 12, 12, 13, 14, 16, 18. Step 4: Count the number of observations: n = 6, which is even. Step 5: For even n, the median is the average of the n/2 th and (n/2 + 1) th terms. Step 6: Here n/2 = 3, so we take the 3rd and 4th terms in the ordered list. Step 7: The 3rd term is 13 and the 4th term is 14. Step 8: Median = (13 + 14) / 2. Step 9: Compute the average: 27 / 2 = 13.5. Step 10: So, the median of the given numbers is 13.5.

Verification / Alternative check:
We can cross check by understanding the definition. Half the numbers should be less than or equal to the median and half greater than or equal to the median. In our ordered list 12, 12, 13, 14, 16, 18, there are three values (12, 12, 13) that are less than or equal to 13.5 and three values (14, 16, 18) that are greater than or equal to 13.5. This confirms that 13.5 is correctly positioned as the central value.

Why Other Options Are Wrong:
Option A (13): This is one of the middle numbers but not the average of the two middle values. Option B (14): The other middle number, again not averaged. Option C (14.5): Too high; it is not the mean of 13 and 14. Option E (15): Lies outside the central gap and is not tied to the positions of the data points.

Common Pitfalls:
Some learners forget to sort the data before finding the median or mistakenly pick just one of the two central values in an even sized data set. Others confuse median with mean and attempt to sum all numbers and divide by 6 instead. Carefully arrange the data and apply the right rule for the even number of observations to avoid such mistakes.

Final Answer:
The median of the given six numbers is 13.5.