The average of 10 observations is 46. It was realised later that an observation was misread as 42 in place of

Question

The average of 10 observations is 46. It was realised later that an observation was misread as 42 in place of 142. Find the correct average.

Examoogle · Accepted Answer

The correct answer is Option A: 56. Calculate the net change in sum: $142 - 42 = +100$. Divide by the number of observations ($10$) to find the change in average: $\frac{100}{10} = +10$. Add this to the incorrect average: $46 + 10 = 56$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the net change in sum: $142 - 42 = +100$. Divide by the number of observations ($10$) to find the change in average: $\frac{100}{10} = +10$. Add this to the incorrect average: $46 + 10 = 56$.

Formula Used: $$	ext{Correct Average} = \frac{	ext{Incorrect Sum} - 	ext{Incorrect Value} + 	ext{Correct Value}}{	ext{Total Observations}}$$

Given: Number of observations = 10, Incorrect average = 46, Incorrect observation = 42, Correct observation = 142

Steps: Calculate Incorrect Sum: Find the total sum of the 10 observations using the incorrect average: $	ext{Sum} = 10 	imes 46 = 460$.. Adjust the Sum: Subtract the wrongly read observation ($42$) and add the correct observation ($142$) to the incorrect sum.. Calculate Correct Average: Divide the corrected sum by the total number of observations ($10$).

Answer: A is correct because the corrected average calculated as 56 matches Option A.

Exam Tip: This technique of adjusting sums directly is also frequently used in weighted averages and statistics problems involving missed data points.

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