SUMMARISING AND PRESENTING DATA

MEASURES OF VARIABILITY

Comments

1. MINITAB command is STDEV C1 and standard deviation is also given, with other values, by DESCRIBE C1.

   

2. Although (n-1) is most commonly used for the denominator, sometimes n is used. Many calculators have both versions - usually the one with n is (wrongly) called s and the one with (n-1) is called s. Some textbooks start using n and then change to (n-1). (eg Staudte's "Seeing Through Statistics".)
3. An alternative version of the formula which is easier to use is
   
   e.g. for data set A, n=7
   
4. For grouped data with values and corresponding frequencies the formula is
   

   EXAMPLE - for the student age data
   For the student age data (x_i = age of student, f_i = number of students with age x_i)
   

   Boxplots

5. The standard deviation, like the mean, is strongly influenced by extreme values. eg Commodore Prices
   

The MINITAB command

For all Commodore prices

Omitting the value $29,500

If an observation is more than 3 times the interquartile range (IQR) from an end of the box, it is the MINITAB convention to regard it as an "outlier" (possibly a mistake?) and it is marked as o on a box plot. If an observation is between 1.5 x IQR and 3 x IQR from one end of the box, it is a possible outlier. It is marked as * on a box plot. The whiskers of the boxplot do not extend to the *'s and o's.

Five-number summary

minimum, Q1, M, Q3, maximum

This provides a quick overall description of a distribution.