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

Introduction / Context:
This question belongs to the topic of measures of central tendency in statistics, specifically the median. Unlike the mean, which is an arithmetic average, the median is the middle value when data are arranged in ascending or descending order. You are given six numbers and asked to find their median. Such simple median questions regularly appear in school exams and basic aptitude tests.

Given Data / Assumptions:
- The given numbers are 14, 12, 12, 16, 13 and 18.
- We assume that each value represents one observation and that no value has extra weight beyond its appearance in the list.
- We must compute the median of these six numbers.

Concept / Approach:
The median of a data set is the middle value when the observations are arranged in order. For an odd number of observations, the median is the single middle term. For an even number of observations, as in this case with six values, the median is the average of the two central terms after sorting. Therefore, our approach is to sort the data, identify the two middle values and then compute their mean.

Step-by-Step Solution:
Step 1: List the data: 14, 12, 12, 16, 13 and 18.Step 2: Arrange these values in ascending order: 12, 12, 13, 14, 16, 18.Step 3: Count the number of observations. There are 6 observations, which is an even number.Step 4: For an even number of observations, the median is the average of the 3rd and 4th values in the ordered list.Step 5: Identify the 3rd value: 13.Step 6: Identify the 4th value: 14.Step 7: Compute the median = (13 + 14) / 2 = 27 / 2 = 13.5.Step 8: Therefore, the median of the given data set is 13.5.

Verification / Alternative check:
You can think of the median as the value that has an equal number of observations on either side when sorted. In the ordered list 12, 12, 13, 14, 16, 18, the two central positions are between 13 and 14. There are two values below 13 and two values above 14, so the midpoint between 13 and 14 is the correct median. That midpoint is 13.5, confirming our earlier calculation.

Why Other Options Are Wrong:
Values such as 13 or 14 correspond to one of the central terms but ignore the fact that the sample size is even. The median must be the average of the two central values, not just one of them. Values like 14.5 or 15 do not represent the midpoint between 13 and 14 and therefore cannot be the correct median for this particular data set.

Common Pitfalls:
A frequent mistake is to forget to sort the data before finding the median. Another common error is to pick either the 3rd or 4th observation alone when there are an even number of data points, instead of averaging the two central ones. Always remember to order the data and, for an even count, compute the mean of the two middle observations.

Final Answer:
The median of the numbers 14, 12, 12, 16, 13 and 18 is 13.5.