Question:
<p>The mean weight per student in a group of seven students is 55 kg. If the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is</p>
<p>(1) 55 kg</p>
<p>(2) 60 kg</p>
<p>(3) 57 kg</p>
<p>(4) 50 kg</p>
Step-by-Step Solution
Key Concept: Use the definition of mean: Mean = (Sum of all observations)/(Number of observations). Rearrange to find the unknown value by multiplying mean by total count and subtracting known values.
<p><strong>Step 1:</strong> Write the formula for mean.</p><p>Mean = (Sum of all weights)/(Number of students)</p><p><strong>Step 2:</strong> Substitute known values.</p><p>55 = (Sum of 7 weights)/7</p><p><strong>Step 3:</strong> Calculate total sum of all 7 weights.</p><p>Sum of 7 weights = 55 × 7 = 385 kg</p><p><strong>Step 4:</strong> Find sum of 6 known weights.</p><p>Sum of 6 weights = 52 + 58 + 55 + 53 + 56 + 54 = 328 kg</p><p><strong>Step 5:</strong> Calculate the seventh student's weight.</p><p>Weight of 7th student = 385 - 328 = 57 kg</p><p>∴ Answer: C (57 kg)</p>
Correct Answer: C