Sale-price observations are $410,000, $425,000, $410,000, $440,000, $410,000. Compute the mode; use the uniquely most frequent observation. Report to the nearest dollar.
Correct Answer
D) $410,000
410000 occurs 3 times; every other distinct observation occurs less often.
Why This Is the Correct Answer
Option D is correct because $410,000 occurs three times in the data, more often than any other value; $425,000 and $440,000 each occur once. The mode is the uniquely most frequent observation, so it is $410,000.
Why the Other Options Are Wrong
Option A: $419,000
Option A, $419,000, is the arithmetic mean: ($410,000 + $425,000 + $410,000 + $440,000 + $410,000) / 5 = $2,095,000 / 5 = $419,000. The mode is the most frequent value, $410,000.
Option B: $440,000
Option B, $440,000, is the highest observation and occurs only once. The mode is $410,000, which occurs three times.
Option C: $425,000
Option C, $425,000, is the mid-range, the average of the lowest and highest prices: ($410,000 + $440,000) / 2 = $425,000. It also happens to be a price that occurs only once, so it is not the mode; $410,000 occurs three times.
Mode means most
Mode and most both start with "mo": the mode is the value that shows up most often.
How to use: Use this to separate the mode from the mean, median and mid-range when reading summary statistics.
Exam Tip
For a mode question, count how many times each value appears; there is nothing to add or divide.
Common Mistakes to Avoid
- -Computing the mean when the mode is asked for
- -Averaging the highest and lowest values (the mid-range)
- -Picking the largest value instead of the most frequent one
Concept Deep Dive
Analysis
This question tests identifying the mode, the most frequently occurring value. Among $410,000, $425,000, $410,000, $440,000 and $410,000, the value $410,000 appears three times while the others appear once. The distractors are other measures of location, such as the mean and mid-range, or simply the highest price.
Background Knowledge
The mode is the value that occurs most often in a data set. A data set can have one mode, several modes or none if no value repeats. The mean, median and mid-range are other measures of location, each computed differently.
Real-World Application
In a subdivision, three of five recent sales closed at $410,000 because they were the same floor plan from one builder. The appraiser notes $410,000 as the most common price while also reporting the mean and median to describe the market.
More Statistics Questions
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First quartile Q1 is $390,000 and third quartile Q3 is $470,000. Compute the midhinge (Q1+Q3)/2 to the nearest dollar.
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An appraiser gives reliability weights of 2, 2 and 1 to sale prices of $580,000, $560,000 and $540,000, respectively. What is the weighted mean price, to the nearest dollar?