Statistics
RD Sharma
CBSE
Grade 10
Question:
The mean of the following data is $50$. Find the value of $p$:
Class: 0-20, 20-40, 40-60, 60-80, 80-100
Frequency: 17, p, 32, 24, 19
Step-by-Step Solution
Key Concept: $x_i$: 10, 30, 50, 70, 90. $\sum f = 92 + p$.<br>$\sum f x = 170 + 30p + 1600 + 1680 + 1710 = 5160 + 30p$.<br>$\dfrac{5160 + 30p}{92 + p} = 50 \Rightarrow 5160 + 30p = 4600 + 50p \Rightarrow 20p = 560 \Rightarrow p = 28$.
$\sum f = 92 + p, \sum f x = 5160 + 30p$. [1.0 Mark]
$5160 + 30p = 4600 + 50p \Rightarrow 20p = 560 \Rightarrow p = 28$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Calculating $\sum f$ and $\sum fx$: 1.0 Mark
Solving $p = 28$: 2.0 Marks
Correct Answer:
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