The following sale prices were recorded: $285,000, $295,000, $275,000, $285,000, $305,000. What is the mode?
Correct Answer
C) $285,000
Why this is correct: The mode is the most frequently occurring value. In the set ($285,000, $295,000, $275,000, $285,000, $305,000), $285,000 appears twice, while all others appear once. Why the other choices are wrong: $30,000 is the range, not a sale price. $295,000 appears only once. $289,000 is the mean (average), not the mode. Exam tip: To find the mode, scan the list for the number that repeats most often.
Why This Is the Correct Answer
Option A ($285,000) is correct because it appears twice in the dataset, making it the most frequently occurring value. When examining the sale prices $285,000, $295,000, $275,000, $285,000, $305,000, we can see that $285,000 appears in both the first and fourth positions. All other values ($295,000, $275,000, and $305,000) appear only once each. By definition, the mode is the value with the highest frequency of occurrence, which is clearly $285,000.
Why the Other Options Are Wrong
Option A: $30,000
$30,000 is the range of the dataset (difference between highest and lowest values: $305,000 - $275,000), not the mode. This represents the spread of the data, not the most frequently occurring value.
Option B: $295,000
$295,000 appears only once in the dataset, so it cannot be the mode. While it is one of the sale prices recorded, it has the same frequency as $275,000 and $305,000, making it less frequent than $285,000.
Option D: $289,000
$289,000 is the mean (average) of the dataset, not the mode. This value is calculated by adding all sale prices and dividing by the number of sales, but it doesn't represent the most frequently occurring value.
MODE = Most Often Data Entry
Remember MODE as 'Most Often Data Entry' - the value that shows up the MOST OFTEN in your data entries. Think of it as the 'popular kid' in the dataset who appears more frequently than anyone else.
How to use: When you see a mode question, immediately start counting how many times each value appears. Look for the 'popular kid' - the number that shows up most often. Don't calculate averages or find middle values; just count frequencies.
Exam Tip
Quickly organize the data in ascending order and mark frequency counts next to each unique value. This visual approach prevents errors and makes the mode immediately apparent.
Common Mistakes to Avoid
- -Calculating the mean instead of identifying the most frequent value
- -Confusing mode with median by looking for the middle value
- -Selecting the range or other statistical measure instead of frequency count
Concept Deep Dive
Analysis
This question tests understanding of the mode, one of the three primary measures of central tendency used in real estate appraisal statistics. The mode represents the most frequently occurring value in a dataset and is particularly useful when analyzing categorical data or when the most common value is more meaningful than the average. In real estate appraisal, the mode can help identify the most typical sale price in a neighborhood or the most common property feature. Unlike mean and median, the mode focuses on frequency rather than mathematical center, making it valuable for understanding market patterns and buyer preferences.
Background Knowledge
Measures of central tendency include mean (average), median (middle value), and mode (most frequent value), each serving different analytical purposes in real estate appraisal. The mode is particularly useful when dealing with categorical data or when the most common occurrence is more relevant than mathematical averages.
Real-World Application
Appraisers use mode to identify the most common sale price range in a neighborhood, helping determine typical market expectations. For example, if most homes sell around $285,000, this mode value indicates the price point most acceptable to buyers in that market segment.
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