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Statistics
RD Sharma
CBSE
Grade 10

Question:

If the mean of 5 observations is 12 and their variance is 4, and if 2 is multiplied to each observation, find the new mean and new variance.

Step-by-Step Solution

Key Concept: Multiplying each observation by $k=2$ multiplies the mean by $k$ and variance by $k^2$.<br>New Mean $= 12 \times 2 = 24$.<br>New Variance $= 4 \times 2^2 = 16$.
$\text{New Mean} = 12 \times 2 = 24$. [1.5 Marks]
$\text{New Variance} = 4 \times 2^2 = 16$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Evaluating new mean $= 24$: 1.5 Marks
Evaluating new variance $= 16$: 1.5 Marks

Correct Answer:
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