Lq

What Lq is

Lq is a measure of statistical dispersion that is used to compare the spread of two or more sets of data. It is similar to the commonly used measure of variance, but is more appropriate for data sets that may include outliers or values that are outliers relative to the rest of the data set.

Steps for Calculating Lq:

  1. Calculate the median of each data set.
  2. Calculate the interquartile range (IQR) of each data set.
  3. Calculate Lq by taking the ratio of the IQRs of the two data sets.
  4. The larger the ratio, the greater the difference in the spread of the data sets.

Examples

  1. Lq statistics are commonly used to measure the uniformity of a sample. This is done by calculating the ratio of the largest observation to the smallest observation in the sample.

  2. Lq statistics can be used to compare the skewness of a sample. This is done by calculating the ratio of the third and first quartiles.

  3. Lq statistics can be used to estimate the standard deviation of a sample. This is done by calculating the ratio of the third and first quartiles and then multiplying it by 1.34 times the interquartile range.

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