Five sale prices are $200,000, $210,000, $220,000, $230,000 and $240,000. Add one sale at $1,000,000. What are the new mean and median?
Correct Answer
A) Mean $350,000; median $225,000
Original mean and median are both $220,000. Adding $1,000,000 gives total $2,100,000 across 6 observations, mean $350,000. The median becomes the average of $220,000 and $230,000, or $225,000. These data illustrate differential sensitivity; no universal magnitude comparison follows for every possible sample.
Why This Is the Correct Answer
Option A is correct because the new total is $1,100,000 + $1,000,000 = $2,100,000 across 6 sales, giving a mean of $350,000. With six ordered values, the median is the average of the third and fourth, ($220,000 + $230,000) ÷ 2 = $225,000. This illustrates that the mean is affected more by extreme values than the median.
Why the Other Options Are Wrong
Option B: Mean $220,000; median $350,000
Option B, mean $220,000 and median $350,000, reports the original mean and puts the new mean in the median's place. The new mean is $2,100,000 ÷ 6 = $350,000 and the new median is $225,000.
Option C: Mean $350,000; median $350,000
Option C, mean $350,000 and median $350,000, gets the mean right but wrongly treats the median as moving the same way. The median is the average of the two middle values, ($220,000 + $230,000) ÷ 2 = $225,000.
Option D: Mean $225,000; median $220,000
Option D, mean $225,000 and median $220,000, uses the new median as the mean and the original median as the median. The correct figures are mean $2,100,000 ÷ 6 = $350,000 and median $225,000.
Mean moves, median stays
One giant sale drags the mean toward it but barely nudges the median.
How to use: Use this to predict which measure shifts more when an outlier is added.
Exam Tip
After adding an observation, recount n and find the new middle position; with an even count the median is the average of the two central values.
Common Mistakes to Avoid
- -Assuming the median shifts as much as the mean
- -Forgetting to update n after adding an observation
- -Swapping the mean and median values
Concept Deep Dive
Analysis
This question tests how an extreme value affects the mean compared with the median. Adding a $1,000,000 sale to five sales averaging $220,000 shifts the mean sharply, while the median moves only slightly. The answer requires recomputing both measures with six observations.
Background Knowledge
The median depends only on the middle position of ordered data, so a single extreme value shifts it little. The mean incorporates every value's magnitude, so outliers pull it strongly. This is why the median is often preferred for skewed price data.
Real-World Application
In a neighborhood of modest homes, one estate sells for $1,000,000. An appraiser notes that the mean sale price jumps well above typical prices, so the median gives a better picture of what ordinary homes are selling for.
More Statistics Questions
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Previous Question
Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
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Three ratio/price pairs are 0.85/$80,000,0.95/$200,000 and 1.10/$400,000. Define PRD as mean ratio divided by sale-price-weighted mean ratio. Which rounded PRD and observed sample tendency follow?