The following sale prices were recorded: $250,000, $260,000, $255,000, $270,000, $255,000. What is the median sale price?
Correct Answer
A) $255,000
The median is the middle value when data is arranged in order. Arranged: $250,000, $255,000, $255,000, $260,000, $270,000. The middle value is $255,000.
Why This Is the Correct Answer
The median is the middle value when data points are arranged in ascending order. With five sale prices ($250,000, $255,000, $255,000, $260,000, $270,000), the third value is the median. Since there are an odd number of values (5), the median is simply the middle position, which is $255,000. This represents the central tendency of the data set.
Why the Other Options Are Wrong
Option B: $258,000
$258,000 appears to be calculated as the mean (average) of the data set. The mean is found by adding all values ($1,290,000) and dividing by the count (5), which equals $258,000. However, the question asks for the median, not the mean. These are different measures of central tendency.
Option C: $260,000
$260,000 is the fourth value in the ordered data set, not the median. This error occurs when someone incorrectly identifies the middle position in an odd-numbered data set. The median for five values is the third position, not the fourth.
Option D: $250,000
$250,000 is the lowest value in the data set, not the median. This represents the minimum value rather than the middle value. Someone might confuse this with other statistical measures or simply misunderstand what median means.
Memory Technique
Remember 'MEDIAN = MIDDLE' - arrange data in order, then find the exact center. For odd numbers of values, it's the middle position. For even numbers, average the two middle values.
Exam Tip
Always arrange data in ascending order first, then count to find the exact middle position for median calculations.
Common Mistakes to Avoid
- -Confusing median with mean (average)
- -Miscounting the middle position in ordered data
- -Using the data without first arranging it in order
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