Chapter 5: Descriptive Measures Of Spread Flashcards
What is a measure of spread
A measure of spread attempts to portray, by a single value, how widely data is distributed over the domain of the data
Name the four measures of spread
Range
Interquartile range
Quartile deviation
Standard deviation
Coefficient of variation
What are the properties of range
The range is a simple statistic and it’s easy to calculate
The range is extremely sensitive to outliers
It is based on only two values which are often extreme values. This measure does not take into account the variation of the other values
What is the interquartile range
It is the difference between the third quartile and the first quartile
Q3-Q1
What is quartile deviation
The quartile deviation is a measure of spread based on the interquartile range.
The quartile deviation is equal to half of the difference between the third and first quartile
Q3-Q1/2
What are the properties of the interquartile range and the quartile deviation
The quartile range is easy to calculate and it is based on values which are not extreme or outlier values
The quartile range is a useful measure of spread if the data contains outliers, since the bottom 25% and the top 25% of the ordered observations are ignored
The quartile deviation has the drawback that only some of the values are used to evaluate this measure. A large amount of the information included in the data set is therefore excluded when the quartile deviation is determined
What is standard deviation
Standard deviation is the measure of spread which is used most in statistical practice.
The standard deviation tries to potray the average distance of the observations from the arithmetic mean of observations
What are the properties of standard deviation
Standard deviation is the most usable and trustworthy measure of spread, since it takes in account all the observations
However, because this measure is based on all the observations it is sensitive to outliers
Standard deviation possess a manageable mathematical properties
What is the best known relative measure of spread
Coefficient of variation
What is the five number summary
It is the minimum, Q1, median, Q3, maximum
