Statistics
Mean
Grade None
Question:
<p>In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what is the average of the girls?</p>
<p>73</p>
<p>65</p>
<p>68</p>
<p>74</p>
Step-by-Step Solution
Key Concept: Use the weighted average formula: total marks of class = total marks of boys + total marks of girls. The average of girls can be found by rearranging this equation to isolate the sum of girls' marks.
<p><strong>Step 1:</strong> Calculate total marks of 70 boys.</p><p>Total marks of boys = 70 × 75 = 5250</p><p><strong>Step 2:</strong> Calculate total marks of entire class of 100 students.</p><p>Total marks of class = 100 × 72 = 7200</p><p><strong>Step 3:</strong> Find total marks of girls (100 - 70 = 30 girls).</p><p>Total marks of girls = 7200 - 5250 = 1950</p><p><strong>Step 4:</strong> Calculate average marks of girls.</p><p>Average of girls = 1950 ÷ 30 = 65</p><p>∴ Answer: B (Average of girls = 65)</p>
Correct Answer: B