The average of 9 observations was found to be 35. Later on, it was detected that an observation 81 was misread as 18. The correct average of the observations is:
42
Understanding the Problem:
The problem involves calculating the correct average of 9 observations after correcting a misread value. Initially, the average of 9 observations was calculated as 35. This means the sum of these 9 observations was \(9 \times 35 = 315\).
Correcting the Error:
An observation was misread as 18 instead of the correct value 81. This means that the initial sum of 315 was \(81 - 18 = 63\) less than the actual sum. Therefore, the correct sum of the observations is \(315 + 63 = 378\).
Calculating the Correct Average:
The correct average is found by dividing the correct sum by the number of observations (9): \(378 \div 9 = 42\).
Therefore, the correct average of the observations is 42.
The solution involves understanding the concept of averages and how to adjust for errors in the data. By determining the difference between the misread and correct values, we can accurately correct the initial sum and obtain the correct average. This demonstrates a thorough understanding of data analysis and calculation.
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