The mean marks for 30 students are 58.5. If 75 was mistakenly logged as 57, determine the correct mean.
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Answer: D. 59.1
Explanation
The total marks sum for thirty students is found by multiplying thirty by the mean of fifty eight point five. The net error is calculated by subtracting the mistakenly logged value of fifty seven from the correct value of seventy five, yielding eighteen. Adding this positive error of eighteen to the total sum and dividing by thirty students gives a corrected mean of fifty nine point one. The arithmetic mean is sensitive to data entry errors because it depends on the sum of all values. Correcting a dataset involves adjusting the total sum by the net difference and recalculating the average. Statistical accuracy is essential for maintaining reliable data summaries in institutional records.
Option A underestimates the corrected mean by failing to apply the full positive error adjustment. Option B represents an incorrect adjustment that does not account for the proper distribution across students. Option C is slightly too low and results from a minor miscalculation in the average increase.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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