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The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations?
- a)5
- b)10
- c)15
- d)45
Correct answer is option 'D'. Can you explain this answer?
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The variance of 20 observations is 5. If each observation is multiplie...
New variance = 5 × (3)2 = 45
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The variance of 20 observations is 5. If each observation is multiplie...
Given:
- Variance of 20 observations = 5
To find:
- Variance of the resulting observations when each observation is multiplied by 3
Solution:
We know that variance is a measure of how spread out the data is from the mean.
Variance is calculated using the formula:
Variance = (sum of (x - mean)^2) / n
where x is the observation, mean is the average of all observations, and n is the number of observations.
When each observation is multiplied by a constant (in this case, 3), the mean also gets multiplied by the same constant.
Let's say the original observations are x1, x2, x3, ..., x20.
Then the new observations will be 3x1, 3x2, 3x3, ..., 3x20.
The new mean will be:
New mean = (3x1 + 3x2 + ... + 3x20) / 20
= 3(x1 + x2 + ... + x20) / 20
= 3(mean)
So, the new variance can be calculated using the formula:
New variance = (sum of (3x - 3*mean)^2) / 20
= (9 * sum of (x - mean)^2) / 20
= 9 * variance
= 9 * 5
= 45
Therefore, the new variance of the resulting observations is 45.
Answer: (d) 45
- Variance of 20 observations = 5
To find:
- Variance of the resulting observations when each observation is multiplied by 3
Solution:
We know that variance is a measure of how spread out the data is from the mean.
Variance is calculated using the formula:
Variance = (sum of (x - mean)^2) / n
where x is the observation, mean is the average of all observations, and n is the number of observations.
When each observation is multiplied by a constant (in this case, 3), the mean also gets multiplied by the same constant.
Let's say the original observations are x1, x2, x3, ..., x20.
Then the new observations will be 3x1, 3x2, 3x3, ..., 3x20.
The new mean will be:
New mean = (3x1 + 3x2 + ... + 3x20) / 20
= 3(x1 + x2 + ... + x20) / 20
= 3(mean)
So, the new variance can be calculated using the formula:
New variance = (sum of (3x - 3*mean)^2) / 20
= (9 * sum of (x - mean)^2) / 20
= 9 * variance
= 9 * 5
= 45
Therefore, the new variance of the resulting observations is 45.
Answer: (d) 45
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The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations?a)5b)10c)15d)45Correct answer is option 'D'. Can you explain this answer?
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