Question

Briefly define the measures R, Q, and s. What are the advantages of using the standard deviation over range and interquartile range?

Answer 1

Range (R) : The range is the difference between the largest and the smallest observation in the data.

Range = Largest observation - smallest observation

The range is the simplest measure of variability to calculate but can be misleading if the dataset contains extreme values.

Quartiles(Q) : Quartiles in statistics are values that divide your data into quarters.

The first quartile (also called the lower quartile) is the number below which lies the 25 percent of the bottom data. The second quartile (the median) divides the range in the middle and has 50 percent of the data below it. The third quartile (also called the upper quartile) has 75 percent of the data below it and the top 25 percent of the data above it.

Standard deviation (s) : Standard deviation is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. Standard deviation is the square root of sum of squared deviation from the mean divided by the number of observations.

Advantages : The standard deviation is the most robust measure of variability since it takes into account a measure of how every value in the dataset varies from the mean. We can do algebraic operation with standard deviation and it is less affected by fluctuations of sampling than range and IQR. Also it is possible to calculate the combined standard deviation of two or more groups, this is not possible with range and IQR.