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What are the limits of the coefficient of concurrent deviations?
- a)No limit
- b)Between –1 and 0, including the limiting values
- c)Between 0 and 1, including the limiting values
- d)Between –1 and 1, the limiting values inclusive
Correct answer is option 'D'. Can you explain this answer?
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What are the limits of the coefficient of concurrent deviations?a)No l...
Coefficient of concurrent deviations :
A very simple and casual method of finding correlation when we are not serious about the magnitude of the two variables is the application of concurrent deviations.
This method involves in attaching a positive sign for a x-value (except the first) if this value is more than the previous value and assigning a negative value if this value is less than the previous value.
This is done for the y-series as well. The deviation in the x-value and the corresponding y-value is known to be concurrent if both the deviations have the same sign.
Denoting the number of concurrent deviation by c and total number of deviations as m (which must be one less than the number of pairs of x and y values), the coefficient of concurrent-deviations is given by
If (2c–m) > 0, then we take the positive sign both inside and outside the radical sign and if (2c–m) < 0, we are to consider the negative sign both inside and outside the radical sign.
Like Pearson’s correlation coefficient and Spearman’s rank correlation coefficient, the coefficient of concurrent- deviations also lies between –1 and 1, both inclusive.
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What are the limits of the coefficient of concurrent deviations?a)No l...
Limits of the Coefficient of Concurrent Deviations
The coefficient of concurrent deviations is a statistical measure that determines the relationship between two variables. It is calculated by dividing the sum of the products of the deviations of two variables from their respective means by the product of their standard deviations. The limits of the coefficient of concurrent deviations are as follows:
Limit 1: Between 1 and 1, the limiting values inclusive
The coefficient of concurrent deviations can range from -1 to +1, but its limits are between 1 and 1, including the limiting values. This means that the coefficient of concurrent deviations can never be greater than 1 or less than -1. If the coefficient of concurrent deviations is equal to 1 or -1, it indicates a perfect positive or negative relationship between the two variables, respectively.
Limit 2: The coefficient of concurrent deviations cannot be greater than 1
The coefficient of concurrent deviations cannot be greater than 1. This is because a value greater than 1 indicates that the sum of the products of the deviations of two variables from their respective means is greater than the product of their standard deviations. This is not possible, as the product of their standard deviations is always greater than or equal to the sum of the products of the deviations of two variables from their respective means.
Limit 3: The coefficient of concurrent deviations cannot be less than -1
The coefficient of concurrent deviations cannot be less than -1. This is because a value less than -1 indicates that the sum of the products of the deviations of two variables from their respective means is less than the product of their standard deviations. This is not possible, as the product of their standard deviations is always greater than or equal to the sum of the products of the deviations of two variables from their respective means.
Conclusion
In conclusion, the coefficient of concurrent deviations is a useful statistical measure that determines the relationship between two variables. Its limits are between 1 and 1, including the limiting values, and it cannot be greater than 1 or less than -1.
The coefficient of concurrent deviations is a statistical measure that determines the relationship between two variables. It is calculated by dividing the sum of the products of the deviations of two variables from their respective means by the product of their standard deviations. The limits of the coefficient of concurrent deviations are as follows:
Limit 1: Between 1 and 1, the limiting values inclusive
The coefficient of concurrent deviations can range from -1 to +1, but its limits are between 1 and 1, including the limiting values. This means that the coefficient of concurrent deviations can never be greater than 1 or less than -1. If the coefficient of concurrent deviations is equal to 1 or -1, it indicates a perfect positive or negative relationship between the two variables, respectively.
Limit 2: The coefficient of concurrent deviations cannot be greater than 1
The coefficient of concurrent deviations cannot be greater than 1. This is because a value greater than 1 indicates that the sum of the products of the deviations of two variables from their respective means is greater than the product of their standard deviations. This is not possible, as the product of their standard deviations is always greater than or equal to the sum of the products of the deviations of two variables from their respective means.
Limit 3: The coefficient of concurrent deviations cannot be less than -1
The coefficient of concurrent deviations cannot be less than -1. This is because a value less than -1 indicates that the sum of the products of the deviations of two variables from their respective means is less than the product of their standard deviations. This is not possible, as the product of their standard deviations is always greater than or equal to the sum of the products of the deviations of two variables from their respective means.
Conclusion
In conclusion, the coefficient of concurrent deviations is a useful statistical measure that determines the relationship between two variables. Its limits are between 1 and 1, including the limiting values, and it cannot be greater than 1 or less than -1.
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What are the limits of the coefficient of concurrent deviations?a)No limitb)Between –1 and 0, including the limiting valuesc)Between 0 and 1, including the limiting valuesd)Between –1 and 1, the limiting values inclusiveCorrect answer is option 'D'. Can you explain this answer?
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