TEMP

Boxplot

PRACTICE ACTIVITY

An example of comparing the motivation attitude of 2015 HSC performances of the top six courses in NSW high school is in Figure 1.3 below.

Figure 1.3 - Boxplots comparing 2015 HSC performance of the top 6 courses.

Note: The BOSTES' data sources (available at https://www.boardofstudies.nsw.edu.au/ebos/static/BDHSC_2015_12.html) for the above boxplots are collected as follows:

How can we interpret information through the comparison of boxplots?

What decisions can be made from the comparison of the above boxplots ?

With an interpretation, the boxplots in Figure 1.3 show that 

-Mathematics General 2 has the highest level of Median, followed by Biology, then Business Studies, and Mathematics

-English (Standard) has the lowest level of Median, and English (Advanced) has the second last of Median.

Importantly as mentioned, the interquartile range IQR of each box equals the length of that box. 

Further, Levine et al (2009) remind that each box obtains the middle 50% of an ordered array of its data values, and 25% between the median and each quartile. They add that the lower 25% of the data values is represented by a line [a whisker) connecting the bottom [Q1] of the box to the location of the smallest value [Min]. As such, the upper 25% of the data values is represented by a whisker connecting the top [Q3] of the box to the Max.

DISTRIBUTION OF DATASETS - APPLYING LEVINE'S RULES

In each box, by applying Levine et al (2009) rules of three comparisons, the solusions are as follows:

Rule 1: Min to  Median vs Median to Max

        -If the distance from the smallest figure [Min] to the Median is greater than the distance from the Median to the biggest figure [Max], then distribution is left skewed. (Mathematics General 2)

        -If the distance from the smallest figure [Min] to the Median is less than the distance from the Median to the biggest figure [Max], then distribution is right skewed.(English (Standard), English (Advanced), Biology, Business Studies, and Mathematics)

Rule 2: Min to Q1 vs Q3 to Max      

        -If the distance from the smallest figure [Min] to the first quartile [Q1] is greater than the distance from the third quartile [Q3] to the biggest figure [Max], then distribution is left skewed. (Mathematics General 2)

       -If the distance from the smallest figure [Min] to the first quartile [Q1] is less than the distance from the third quartile [Q3] to the biggest figure [Max], then distribution is right skewed.(English (Standard), English (Advanced), Biology, Business Studies, and Mathematics)     

Rule 3: Q1 to Median vs Median to Q3

      -If the distance from the first quartile [Q1] to the Median is greater than the distance from the Median to the third quartile [Q3], then distribution is left skewed. (Mathematics General 2 , and Biology?)      

      -If the distance from the first quartile [Q1] to the Median is less than the distance from the Median to the third quartile [Q3], then distribution is right skewed. (English (Standard), English (Advanced), Business Studies, and Mathematics)

The above practice found that Rule 3 of Levine et al (2009) does not apply for the boxplot of Biology (i.e the distribution of Biology is right skewed if applied Rule 1 & 2, but left skewed if applied rule 3)