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If each observation of a raw data, whose variance is σ2, is multiplied by λ, then the variance of new set is
- a)σ2
- b)λ2σ2
- c)λ + σ2
- d)λ2 + σ2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If each observation of a raw data, whose variance is σ2, is mult...
The variance of the new set would be λ2σ2.
The variance of a set of data is defined as the average of the squared differences between the data points and the mean of the data set. If you multiply each data point by a constant factor λ, then the squared differences will also be multiplied by λ2, and therefore the variance will be multiplied by λ2.
Therefore, the correct answer is (b) λ2σ2.
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Community Answer
If each observation of a raw data, whose variance is σ2, is mult...
Unknown, is denoted as xi, the sample variance can be calculated as follows:
s^2 = Σ(xi - x̄)^2 / (n-1)
where x̄ is the sample mean and n is the sample size.
This formula calculates the sum of squared deviations from the mean, divides by the degrees of freedom (n-1), and provides an estimate of the population variance.
Note that when the population variance is known, the formula for the sample variance is slightly different:
s^2 = Σ(xi - μ)^2 / n
where μ is the population mean.
s^2 = Σ(xi - x̄)^2 / (n-1)
where x̄ is the sample mean and n is the sample size.
This formula calculates the sum of squared deviations from the mean, divides by the degrees of freedom (n-1), and provides an estimate of the population variance.
Note that when the population variance is known, the formula for the sample variance is slightly different:
s^2 = Σ(xi - μ)^2 / n
where μ is the population mean.
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If each observation of a raw data, whose variance is σ2, is multiplied by λ, then the variance of new set isa)σ2b)λ2σ2c)λ + σ2d)λ2 + σ2Correct answer is option 'B'. Can you explain this answer?
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