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The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new varianve of the resulting observations ?
- a)5
- b)10
- c)20
- d)40
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The variance of 20 observations is 5. If each observation is multiplie...
Let x1, x2, , x20 be the given observations.
To find variance of2x1, 2x2,2x3,...., 2x20,
Let
denotes the mean of new observation,
Clearly,
Now, variance of new observation
To find variance of2x1, 2x2,2x3,...., 2x20,
Let
denotes the mean of new observation,Clearly,
Now, variance of new observation
Most Upvoted Answer
The variance of 20 observations is 5. If each observation is multiplie...
Variance is a measure of how spread out the data values are in a dataset. It quantifies the average squared deviation of the data points from the mean.
Given that the variance of 20 observations is 5, we can assume that the observations are drawn from a population with a normal distribution.
Let's denote the original observations as X and the new observations (after multiplying each observation by 2) as Y.
To find the new variance of the resulting observations, we need to calculate the variance of Y.
We know that multiplying each observation by a constant (in this case, 2) does not change the shape of the distribution, but it does affect the spread of the data.
Multiplying each observation by 2 scales the data values by a factor of 2, which in turn scales the variance by the square of that factor. Therefore, the new variance of Y will be 4 times the original variance of X.
Mathematically, we can express this relationship as follows:
Var(Y) = 4 * Var(X)
Since the original variance of X is given as 5, we can substitute this value into the equation:
Var(Y) = 4 * 5
= 20
Hence, the new variance of the resulting observations is 20.
Therefore, the correct answer is option C) 20.
Given that the variance of 20 observations is 5, we can assume that the observations are drawn from a population with a normal distribution.
Let's denote the original observations as X and the new observations (after multiplying each observation by 2) as Y.
To find the new variance of the resulting observations, we need to calculate the variance of Y.
We know that multiplying each observation by a constant (in this case, 2) does not change the shape of the distribution, but it does affect the spread of the data.
Multiplying each observation by 2 scales the data values by a factor of 2, which in turn scales the variance by the square of that factor. Therefore, the new variance of Y will be 4 times the original variance of X.
Mathematically, we can express this relationship as follows:
Var(Y) = 4 * Var(X)
Since the original variance of X is given as 5, we can substitute this value into the equation:
Var(Y) = 4 * 5
= 20
Hence, the new variance of the resulting observations is 20.
Therefore, the correct answer is option C) 20.
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The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new varianve of the resulting observations ?a)5b)10c)20d)40Correct answer is option 'C'. Can you explain this answer?
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