• SoniaSamipillai

Descriptive Statistics - Measures of Relative Location - Part1

Updated: Jan 26



The search for truth is more precious than its possession.

Measures of Relative Locations


Measures of relative standing, or relative locations are measures that can be used to compare values from different data sets, or to compare values within the same data set. Measures of relative location helps us to determine how far a particular value is from the mean. The most common ones are :

  1. Quartile

  2. Percentile

  3. Z-Score

  4. Minimum

  5. Maximum

There are two data summaries that are used widely. They are:

  1. Five Number Summary

  2. Seven Number Summary

Percentile


A percentile provides information about how the data are spread over the interval from the smallest value to the largest value.The pth percentile is a value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value.


Calculating the pth percentile

  1. Arrange the data in ascending order(smallest value to largest value)

  2. Compute an index i where i = (p/100)^n where p is the percentile of interest and n is the number of observations.

  3. After step2, if the result, i if its not an integer, round up. The next integer greater than i denotes the position of the pth percentile.

  4. If i is an integer, the pth percentile is the average of the value in the positions i and i+1


Quartile


The 25th, 50th and 75th percentiles, referred to as the first quartile, second quartile(median) and third quartile, respectively. The quartiles can be used to divide a dataset into four parts, with each part containing approximately 25% of the data. Follow the same formula used for calculating percentiles. use p = 25, p = 50 and p = 75


Z-Score


A value computed by dividing the deviation about the mean(xi-xbar) by the standard deviation. A z score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean.

A z-score greater than zero occurs when observations have values greater than mean; A z-score lesser than zero occurs when observations have value less than the mean and when observations have values equal to mean, z-score is zero.


Minimum and Maximum


Five Number Summary


A technique that uses five numbers to summarize the data. The Five numbers are :

  1. Minimum , The smallest value

  2. First Quartile

  3. Second Quartile or Median

  4. Third Quartile

  5. Maximum, The largest value


Seven Number Summary


A technique that uses seven numbers to summarize the data. The Seven Numbers are:

  1. The 2nd percentile

  2. The 9th percentile

  3. The 25th percentile or lower quartile or first quartile

  4. The 50th percentile or median (middle value, or second quartile)

  5. The 75th percentile or upper quartile or third quartile

  6. The 91st percentile

  7. The 98th percentile

While analyzing data, the analyst looks at various different measures to understand the data better. We discussed on the measures of location, dispersion or variability,relative location so far. In the next upcoming blogs, we will also look at the measures of shape and how to detect outliers.


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