Statistics
RD Sharma
CBSE
Grade 10
Question:
If the mean of $x_1, x_2, \dots, x_n$ is $\bar{x}$, show that the mean of $a x_1, a x_2, \dots, a x_n$ is $a \bar{x}$.
Step-by-Step Solution
Key Concept: $\text{New Mean} = \dfrac{\sum a x_i}{n} = \dfrac{a \sum x_i}{n} = a \bar{x}$. Proved!
$\text{New Mean} = \dfrac{\sum (a x_i)}{n} = a \left(\dfrac{\sum x_i}{n}\right)$. [1.0 Mark]
$= a \bar{x}$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Taking constant $a$ out of summation: 1.0 Mark
Proving new mean $= a \bar{x}$: 1.0 Mark
Correct Answer:
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