Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.
The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:
Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.
The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:
1. C.D. based upon range = `(L-S)/(L+S)` , where L and S are Largest and Smallest observation in the series.
2. C.D. based upon quartile deviation = `(Q3 - Q1)/(Q3 + Q1)`
`3. `C.D. based upon Standard deviation = `sigma/barx`
Definition of Coefficient of Variance
Coefficient of variance i.e. Coefficient of Variation is a relative measure for standard deviation. It is defined as 100 times the coefficient of dispersion based upon standard deviation is called coefficient of variation (C.V.), i.e.,
C.V. = `sigma/barx` x 100 .
Since it is relative measure C.V. is used to compare consistency of figures or variability of figures.
Remarks:
1. Less C.V. indicate the less variability or more consistency.
2. More C.V. indicate the more variability or less consistency.
3. According to Karl Pearson who suggested this measure, C.V. is the percentage variation in the mean, standard deviation being considered as the total variation in the mean.
Note:
With the help of C.V. we can find which salesman is more consistent in making sales, which batsman is more consistent in scoring runs, which student is more consistent in scoring marks, which worker is more consistent in production, etc.
I have recently faced lot of problem while learning Interest Compounded, But thank to online resources of math which helped me to learn myself easily on net.
Example of coefficient of variance
An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:
Firm A
Firm B
Number of workers
500
Average daily wages
186 Rs.
175 Rs.
S.D. of daily wages
9 10
In which firm, A or B is more consistent in individual wages?
Solution:
C. V. for firm A = `sigma/barx`` x 100 = 9/186 x 100`
` = 4.84`
C. V. for firm B = `sigma/barx`` x 100 = 10/175 x 100`
` = 5.71`
`Since C.V. for firm B is greater than C.V. for firm A, firm A is more consistent.`
The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:
Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.
The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:
1. C.D. based upon range = `(L-S)/(L+S)` , where L and S are Largest and Smallest observation in the series.
2. C.D. based upon quartile deviation = `(Q3 - Q1)/(Q3 + Q1)`
`3. `C.D. based upon Standard deviation = `sigma/barx`
Definition of Coefficient of Variance
Coefficient of variance i.e. Coefficient of Variation is a relative measure for standard deviation. It is defined as 100 times the coefficient of dispersion based upon standard deviation is called coefficient of variation (C.V.), i.e.,
C.V. = `sigma/barx` x 100 .
Since it is relative measure C.V. is used to compare consistency of figures or variability of figures.
Remarks:
1. Less C.V. indicate the less variability or more consistency.
2. More C.V. indicate the more variability or less consistency.
3. According to Karl Pearson who suggested this measure, C.V. is the percentage variation in the mean, standard deviation being considered as the total variation in the mean.
Note:
With the help of C.V. we can find which salesman is more consistent in making sales, which batsman is more consistent in scoring runs, which student is more consistent in scoring marks, which worker is more consistent in production, etc.
I have recently faced lot of problem while learning Interest Compounded, But thank to online resources of math which helped me to learn myself easily on net.
Example of coefficient of variance
An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:
Firm A
Firm B
Number of workers
500
Average daily wages
186 Rs.
175 Rs.
S.D. of daily wages
9 10
In which firm, A or B is more consistent in individual wages?
Solution:
C. V. for firm A = `sigma/barx`` x 100 = 9/186 x 100`
` = 4.84`
C. V. for firm B = `sigma/barx`` x 100 = 10/175 x 100`
` = 5.71`
`Since C.V. for firm B is greater than C.V. for firm A, firm A is more consistent.`
No comments:
Post a Comment