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The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectively
- a)8 and 20
- b)8 and 4
- c)8 and 8
- d)80 and 40
Correct answer is option 'C'. Can you explain this answer?
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The mean and the variance 10 observations are given to be 4 and 2 resp...
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The mean and the variance 10 observations are given to be 4 and 2 resp...
Mean and Variance of a Dataset:
The mean of a dataset is the average of all the observations in the dataset. It is calculated by summing up all the observations and dividing the sum by the total number of observations. The variance of a dataset is a measure of how spread out the observations are from the mean. It is calculated by taking the average of the squared differences between each observation and the mean.
Given Information:
Mean of the original dataset = 4
Variance of the original dataset = 2
Effect of Multiplying Observations by 2:
When each observation in the dataset is multiplied by a constant, it affects both the mean and the variance of the dataset.
Effect on Mean:
When each observation is multiplied by a constant, the mean of the new dataset is also multiplied by that constant. In this case, since each observation is multiplied by 2, the new mean will be the original mean (4) multiplied by 2, which is 8.
Effect on Variance:
When each observation is multiplied by a constant, the variance of the new dataset is multiplied by the square of that constant. In this case, since each observation is multiplied by 2, the new variance will be the original variance (2) multiplied by the square of 2, which is 2^2 = 4.
Calculating the New Mean and Variance:
Given that the new mean is 8 and the new variance is 4, we can conclude that the correct answer is option C, which states that the mean and variance of the new series are 8 and 8, respectively.
Summary:
- When each observation in a dataset is multiplied by a constant, the mean of the new dataset is also multiplied by that constant.
- When each observation in a dataset is multiplied by a constant, the variance of the new dataset is multiplied by the square of that constant.
- In this case, multiplying each observation by 2 results in a new mean of 8 and a new variance of 4.
- Therefore, the correct answer is option C, which states that the mean and variance of the new series are 8 and 8, respectively.
The mean of a dataset is the average of all the observations in the dataset. It is calculated by summing up all the observations and dividing the sum by the total number of observations. The variance of a dataset is a measure of how spread out the observations are from the mean. It is calculated by taking the average of the squared differences between each observation and the mean.
Given Information:
Mean of the original dataset = 4
Variance of the original dataset = 2
Effect of Multiplying Observations by 2:
When each observation in the dataset is multiplied by a constant, it affects both the mean and the variance of the dataset.
Effect on Mean:
When each observation is multiplied by a constant, the mean of the new dataset is also multiplied by that constant. In this case, since each observation is multiplied by 2, the new mean will be the original mean (4) multiplied by 2, which is 8.
Effect on Variance:
When each observation is multiplied by a constant, the variance of the new dataset is multiplied by the square of that constant. In this case, since each observation is multiplied by 2, the new variance will be the original variance (2) multiplied by the square of 2, which is 2^2 = 4.
Calculating the New Mean and Variance:
Given that the new mean is 8 and the new variance is 4, we can conclude that the correct answer is option C, which states that the mean and variance of the new series are 8 and 8, respectively.
Summary:
- When each observation in a dataset is multiplied by a constant, the mean of the new dataset is also multiplied by that constant.
- When each observation in a dataset is multiplied by a constant, the variance of the new dataset is multiplied by the square of that constant.
- In this case, multiplying each observation by 2 results in a new mean of 8 and a new variance of 4.
- Therefore, the correct answer is option C, which states that the mean and variance of the new series are 8 and 8, respectively.
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The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer?
Question Description
The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer?.
The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer?.
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The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The mean and the variance 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectivelya)8 and 20b)8 and 4c)8 and 8d)80 and 40Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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