Five numbers have a mean of 27. Excluding one number changes the mean to 25. What was the excluded number__________?
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Answer: D. 35
Explanation
Multiplying five numbers by their average mean gives the total sum of one hundred thirty five. Multiplying the remaining four numbers by their new mean gives the sum of one hundred. Subtracting the four number sum from the initial sum isolates the excluded number as thirty five. The arithmetic mean represents the sum of a dataset divided by the count of elements. Total sum of any dataset is always calculated by multiplying the mean by the count. Removing a single value from a dataset proportionally reduces the cumulative total sum.
Data analysts track changing averages over time to identify outlier data points or anomalies. Grade point averages use similar subtraction techniques when adjusting records for dropped test scores. Statistical processing of large datasets often requires updating summary metrics dynamically. Option A suggests twenty five which matches the secondary mean rather than the excluded value. Option C suggests twenty seven which matches the initial mean rather than the missing number. Option D suggests thirty five which correctly completes the mathematical balancing equation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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