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Statistics
RD Sharma
CBSE
Grade 10

Question:

Find the mean of the following distribution using direct method:
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 7, 8, 12, 13, 10

Step-by-Step Solution

Key Concept: Class marks $x_i$: 5, 15, 25, 35, 45.<br>$f_i x_i$: 35, 120, 300, 455, 450.<br>$\sum f_i = 50$, $\sum f_i x_i = 1360$.<br>$\bar{x} = 1360 / 50 = 27.2$.
Class marks $x_i = [5, 15, 25, 35, 45]$. $\sum f_i = 50$. [0.5 Mark]
$\sum f_i x_i = 35 + 120 + 300 + 455 + 450 = 1360$. [1.0 Mark]
$\bar{x} = 1360 / 50 = 27.2$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Finding class marks & $\sum f_i = 50$: 0.5 Mark
Calculating $\sum f_i x_i = 1360$: 1.0 Mark
Evaluating mean $= 27.2$: 0.5 Mark

Correct Answer:
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