Question

Q5. Define the types of correction on the basis of ratio of variation in the variables.

Answer 1

Answer:

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Explanation:

The coefficient of variation (CV) is defined as the ratio of the standard deviation {\displaystyle \ \sigma } to the mean {\displaystyle \ \mu } , {\displaystyle c_{\rm {v}}={\frac {\sigma }{\mu }}.} [1] It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on a ratio scale, that is, scales that have a meaningful zero and hence allow relative comparison of two measurements (i.e., division of one measurement by the other). The coefficient of variation may not have any meaning for data on an interval scale.[2] For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the computed coefficient of variation would be different depending on which scale you used. On the other hand, Kelvin temperature has a meaningful zero, the complete absence of thermal energy, and thus is a ratio scale. In plain language, it is meaningful to say that 20 Kelvin is twice as hot as 10 Kelvin, but only in this scale with a true absolute zero. While a standard deviation (SD) can be measured in Kelvin, Celsius, or Fahrenheit, the value computed is only applicable to that scale. Only the Kelvin scale can be used to compute a valid coefficient of variability.

Measurements that are log-normally distributed exhibit stationary CV; in contrast, SD varies depending upon the expected value of measurements.

A more robust possibility is the quartile coefficient of dispersion, half the interquartile range {\displaystyle {(Q_{3}-Q_{1})/2}} divided by the average of the quartiles (the midhinge), {\displaystyle {(Q_{1}+Q_{3})/2}} .

In most cases, a CV is computed for a single independent variable (e.g., a single factory product) with numerous, repeated measures of a dependent variable (e.g., error in the production process). However, data that are linear or even logarithmically non-linear and include a continuous range for the independent variable with sparse measurements across each value (e.g., scatter-plot) may be amenable to single CV calculation using a maximum-likelihood estimation approach.[3]

Examples

data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as

data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as0 / 100 = 0

data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as0 / 100 = 0A data set of [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as

data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as0 / 100 = 0A data set of [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as10 / 100 = 0.1

data set of [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as0 / 100 = 0A data set of [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as10 / 100 = 0.1A data set of [1, 5, 6, 8, 10, 40, 65, 88] has still more variability. Its standard deviation is 32.90 and its average is 27.9, giving a coefficient of variation of32.90 / 27.9 = 1.18