American Institute of Certified Planners (AICP) Practice Exam

What does the median represent in a data distribution?

1. The average of all observations

2. The score that occurs most frequently

3. The midscore where half the observations fall above and half below

4. The total range of scores

The correct answer is: The midscore where half the observations fall above and half below

The median is defined as the value that divides a data distribution into two equal halves, meaning that half of the observations are below this value and half are above it. This characteristic makes the median particularly useful in statistical analysis, as it is less affected by outliers and skewed data than the mean. In a set of ordered data, if the number of observations is odd, the median is simply the middle number. If the number of observations is even, it is calculated as the average of the two middle numbers. This property highlights the median's role in providing a measure of central tendency that accurately reflects the center of the data distribution, regardless of extreme values. The other options represent different statistical measures. The average, or mean, is the sum of all observations divided by the number of observations and can be heavily influenced by outliers. The mode refers to the most frequently occurring score, which may not provide a representation of the data's center if the distribution is multimodal. Lastly, the total range of scores describes the difference between the highest and lowest values in the data set, which is a measure of spread rather than a central tendency measure.