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The standard deviation of 17 numbers is zero. Then (1980)
- a)the numbers are in geometric progression with common ratio not equal to one.
- b)eight numbers are positive, eight are negative and one is zero.
- c)either (a) or (b)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The standard deviation of 17 numbers is zero. Then (1980)a)the numbers...
If s. d. = 0, statements like (a) and (b) can not be given.
Most Upvoted Answer
The standard deviation of 17 numbers is zero. Then (1980)a)the numbers...
Explanation:
To solve this problem, we need to understand the concept of standard deviation and its relationship with the numbers.
Standard Deviation:
Standard deviation is a measure of how spread out the numbers in a data set are around the mean. It measures the average distance between each data point and the mean of the data set. A larger standard deviation indicates a greater spread or dispersion of the data.
Given:
The standard deviation of 17 numbers is zero.
Implication:
If the standard deviation is zero, it means that all the numbers in the data set are the same, or in other words, there is no variability in the data set. This implies that the numbers are either all equal or in a specific pattern.
Analysis of Options:
a) The numbers are in geometric progression with a common ratio not equal to one:
If the numbers are in a geometric progression with a common ratio not equal to one, it means that each number in the sequence is obtained by multiplying the previous number by a constant ratio. In this case, the standard deviation will not be zero because there will be variability in the data set. Therefore, option 'a' is incorrect.
b) Eight numbers are positive, eight are negative, and one is zero:
If eight numbers are positive, eight are negative, and one is zero, it implies that the numbers have a specific pattern and are not all the same. In this case, the standard deviation will not be zero because there will be variability in the data set. Therefore, option 'b' is incorrect.
c) Either (a) or (b):
Since we have already determined that options 'a' and 'b' are incorrect, option 'c' is also incorrect.
d) None of these:
As we have eliminated all other options, the correct answer must be 'd' - none of these.
Conclusion:
The correct answer is option 'd' - none of these. This is because the standard deviation of zero implies that all the numbers in the data set are the same, and none of the given options satisfy this condition.
To solve this problem, we need to understand the concept of standard deviation and its relationship with the numbers.
Standard Deviation:
Standard deviation is a measure of how spread out the numbers in a data set are around the mean. It measures the average distance between each data point and the mean of the data set. A larger standard deviation indicates a greater spread or dispersion of the data.
Given:
The standard deviation of 17 numbers is zero.
Implication:
If the standard deviation is zero, it means that all the numbers in the data set are the same, or in other words, there is no variability in the data set. This implies that the numbers are either all equal or in a specific pattern.
Analysis of Options:
a) The numbers are in geometric progression with a common ratio not equal to one:
If the numbers are in a geometric progression with a common ratio not equal to one, it means that each number in the sequence is obtained by multiplying the previous number by a constant ratio. In this case, the standard deviation will not be zero because there will be variability in the data set. Therefore, option 'a' is incorrect.
b) Eight numbers are positive, eight are negative, and one is zero:
If eight numbers are positive, eight are negative, and one is zero, it implies that the numbers have a specific pattern and are not all the same. In this case, the standard deviation will not be zero because there will be variability in the data set. Therefore, option 'b' is incorrect.
c) Either (a) or (b):
Since we have already determined that options 'a' and 'b' are incorrect, option 'c' is also incorrect.
d) None of these:
As we have eliminated all other options, the correct answer must be 'd' - none of these.
Conclusion:
The correct answer is option 'd' - none of these. This is because the standard deviation of zero implies that all the numbers in the data set are the same, and none of the given options satisfy this condition.
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The standard deviation of 17 numbers is zero. Then (1980)a)the numbers are in geometric progression with common ratio not equal to one.b)eight numbers are positive, eight are negative and one is zero.c)either (a) or (b)d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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