Karl Pearson co-efficient of variation (CV) measures which of the following characteristics?

Correct option is A

Karl Pearson's coefficient of variation (CV) is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation (σ) to the mean (μ), usually expressed as a percentage:

The CV measures the extent of variability in relation to the mean of the population. It helps in understanding the degree of homogeneity or uniformity of data. A smaller CV indicates data points are closely clustered around the mean, implying higher homogeneity or consistency in the data set. Conversely, a higher CV indicates more variability or heterogeneity.

Thus, the coefficient of variation is a relative measure of dispersion and is primarily used to compare the degree of variation from one data series to another, even if the means are drastically different.

Information Booster:

• Coefficient of Variation (CV) measures homogeneity by assessing relative variability.

• It is a dimensionless number useful for comparing variability between different datasets.

• CV is widely used in fields such as finance, quality control, and meteorology.

• It normalizes standard deviation relative to the mean, making comparisons meaningful.

• A lower CV indicates more uniformity or homogeneity.

• CV is especially useful when the mean values differ significantly.

• It is sensitive to the mean, so it is undefined or meaningless when the mean is zero or close to zero.

Additional Knowledge:

• Unbiasedness (Option b):
  Unbiasedness refers to an estimator whose expected value equals the true parameter value. It is a property of estimators/statistics ensuring no systematic over or underestimation. CV does not measure unbiasedness.

• Consistency (Option c):
  Consistency refers to an estimator that converges in probability to the true parameter value as the sample size increases. CV is not a measure of consistency.

• Efficiency (Option d):
  Efficiency relates to the variance of an estimator among all unbiased estimators — the estimator with the smallest variance is considered most efficient. CV does not measure efficiency.