Question:
<p>The mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50, respectively. The correct mean is</p>
<p>48</p>
<p>82.5</p>
<p>50</p>
<p>80</p>
Step-by-Step Solution
Key Concept: The correct mean is found by adjusting the wrong mean by the total error in readings: subtract the sum of wrong values and add the sum of correct values, then divide by n.
<p><strong>Step 1:</strong> Given wrong mean = 49 for 100 items<br/>∴ Wrong sum of all 100 items = 49 × 100 = 4900</p><p><strong>Step 2:</strong> Identify the reading errors:<br/>• Item 1: Read 40, should be 60 → Error = +20<br/>• Item 2: Read 20, should be 70 → Error = +50<br/>• Item 3: Read 50, should be 80 → Error = +30<br/>Total correction needed = 20 + 50 + 30 = 100</p><p><strong>Step 3:</strong> Calculate correct sum<br/>Correct sum = Wrong sum + Total correction<br/>Correct sum = 4900 + 100 = 5000</p><p><strong>Step 4:</strong> Calculate correct mean<br/>Correct mean = 5000 ÷ 100 = 50</p><p>∴ Answer: C (50)</p>
Correct Answer: C