If the variance of the observations x 1 , x 2 , … … , x n is σ 2 , then the variance of α x 1 , α x 2 , … … , α x n , α ≠ 0 is

Variance = 1 n Σ ( x - x ¯ ) 2 = σ 2 New variance = 1 n Σ ( α x - α x ¯ ) 2 = α 2 1 n Σ ( x - x ¯ ) 2 = α 2 σ 2

Mathematics - Statistics Question with Solution | TestHub

MathematicsStatisticsMeasures of DispersionEasy2 minPYQ_2017

MathematicsEasysingle choice

If the variance of the observations $x_{1}, x_{2}, \dots \dots, x_{n}$ is $σ^{2}$ , then the variance of $α x_{1}, α x_{2}, \dots \dots, α x_{n}, α \neq 0$ is

Options:

Answer:

Solution:

Variance $= \frac{1}{n} Σ (x - \bar{x})^{2} = σ^{2}$

New variance $= \frac{1}{n} Σ (α x - α \bar{x})^{2}$

$= α^{2} \frac{1}{n} Σ (x - \bar{x})^{2} = α^{2} σ^{2}$

Stream:BITSATSubject:MathematicsTopic:StatisticsSubtopic:Measures of Dispersion

⏱ 2mℹ️ Source: PYQ_2017

Doubts & Discussion

Loading discussions...