The following sale prices were recorded: $245,000, $250,000, $250,000, $255,000, $280,000. What is the mode?
Correct Answer
D) $250,000
Why this is correct: The mode is the value that appears most frequently in a data set. In the list $245,000, $250,000, $250,000, $255,000, $280,000, the value $250,000 appears twice, while every other value appears once. Therefore D is correct. Why the other choices are wrong: A, $256,000, is the mean: the sum of $1,280,000 divided by 5. B, $255,000, is one of the sale prices but appears only once, so it is not the mode. C, $35,000, is the range: $280,000 - $245,000. The mode is a frequency measure, not the average or the spread. Exam tip: To find the mode, count frequencies. If no value repeats, there is no mode. Do not confuse the mode with the mean or median.
Why This Is the Correct Answer
Option A ($250,000) is correct because it appears twice in the dataset, making it the most frequently occurring value. When examining the sale prices $245,000, $250,000, $250,000, $255,000, $280,000, only $250,000 repeats. All other values ($245,000, $255,000, and $280,000) appear only once each. By definition, the mode is the value with the highest frequency of occurrence, which is clearly $250,000.
Why the Other Options Are Wrong
Option A: $256,000
Option A ($256,000) represents the mean (average) of the dataset, not the mode. This value is calculated by adding all sales prices and dividing by the number of sales: ($245,000 + $250,000 + $250,000 + $255,000 + $280,000) ÷ 5 = $256,000. The mean and mode are different statistical measures and should not be confused.
Option B: $255,000
Option B ($255,000) is simply one of the sale prices in the dataset that appears only once. This value has no special statistical significance in terms of frequency and does not represent the mode. Students might mistakenly choose this if they confuse the mode with the median or select a middle-appearing value without counting frequencies.
Option C: $35,000
Option C ($35,000) represents the range of the dataset (the difference between the highest and lowest values: $280,000 - $245,000 = $35,000). The range is a measure of dispersion, not central tendency, and has no relationship to the mode. This option tests whether students understand the difference between measures of central tendency and measures of variability.
MODE = Most Often Displayed Entry
Remember MODE as 'Most Often Displayed Entry' - the value that shows up the most times. Think of it like the most popular item in a store window display - it appears most frequently because it sells the most. You can also use 'MODE sounds like MOST' to remember it's about the MOST frequent value.
How to use: When you see a statistics question asking for the mode, immediately start counting how many times each value appears in the dataset. Look for the value that 'shows up MOST' and ignore any mathematical calculations - you're simply counting frequencies, not doing arithmetic.
Exam Tip
Always count the frequency of each value systematically when identifying the mode. Write tally marks next to each unique value as you go through the dataset to avoid missing duplicates, especially in longer lists of comparable sales.
Common Mistakes to Avoid
- -Confusing mode with mean (average) and calculating instead of counting
- -Selecting the median value instead of the most frequent value
- -Choosing the range or another statistical measure instead of identifying frequency
Concept Deep Dive
Analysis
This question tests understanding of the mode, one of the three primary measures of central tendency used in real estate statistics. The mode identifies the most frequently occurring value in a dataset, which is particularly useful in real estate appraisal when analyzing comparable sales data. Unlike mean (average) and median (middle value), the mode focuses on frequency of occurrence rather than mathematical calculation. In real estate markets, the mode can reveal the most common price point in a neighborhood or market segment, providing valuable insight into buyer preferences and market dynamics.
Background Knowledge
Real estate appraisers must understand three measures of central tendency: mean (average), median (middle value when arranged in order), and mode (most frequent value). These statistical tools help analyze comparable sales data and identify market trends. The mode is particularly useful when there are repeated sale prices at specific price points, indicating market preferences or pricing strategies.
Real-World Application
In real estate appraisal, the mode helps identify the most common sale price in a neighborhood, which can indicate the price point most acceptable to buyers in that market. For example, if most homes sell around $250,000, this suggests strong buyer demand and market acceptance at that price level, making it a reliable indicator for valuing similar properties.
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