Statistics
RD Sharma
CBSE
Grade 10
Question:
Find the median for the following distribution:
Wages (in ₹): 60-69, 70-79, 80-89, 90-99, 100-109, 110-119
Workers: 5, 15, 20, 30, 20, 8
Step-by-Step Solution
Key Concept: Continuous boundaries: 59.5-69.5, 69.5-79.5, 79.5-89.5, 89.5-99.5, 99.5-109.5, 109.5-119.5 ($h=10$).<br>$N = 98 \Rightarrow N/2 = 49$. $cf$: 5, 20, 40, 70, 90, 98. Median class $89.5-99.5$ ($l=89.5, cf=40, f=30, h=10$).<br>$\text{Median} = 89.5 + \left(\dfrac{49 - 40}{30}\right) \times 10 = 89.5 + 3 = 92.5$.
Continuous median class $89.5-99.5$ ($l=89.5, cf=40, f=30, h=10$). [1.0 Mark]
$\text{Median} = 89.5 + \left(\dfrac{9}{30}\right) \times 10 = 89.5 + 3 = 92.5$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Converting to continuous boundaries & finding median class: 1.0 Mark
Evaluating median $= 92.5$: 2.0 Marks
Correct Answer:
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