Follow-up of 14 April (Stem-and-Leaf Task): Which part of the Singapore Island has the best air quality?

Claim 1: Air Quality in the eastern part of Singapore is always better than the western part of the island

To investigate this, we are going to compare the quality of air (PSI) in the eastern and western parts of the island. To make comparison for one month is not enough since the air quality varies over the different months in a year (e.g. the wind direction varies in different times of the year).

First, we compare the air quality in the month of October.

• In both zones, the modes do not stand out significantly amongst other days (east with 3 occurences only while the 7 modes identified in the west zone had only 2 occurences). Hence, mode will not be refered to, in this case.
• By comparing the mean, mean PSI for east zone is lower than that of the west. Both zones have 'outliers' (95 and 96 for east and west zones respectively). With reference to the mean, quality of air in east zone is better than that in the west.
• With reference to median, it shows that the east 15 days with PSI less than 33 while the west has less (its median is 38, and it has 11 days enjoying air quality below 33 in the same month)

Hence, based on October 2010's data, quality of air in the east is better than that in the west.

Next, to check for 'consistency' by taking comparing the PSI values in March 2011:

• Comparing the mode, it was 20 at the east (with 5 occurences), which is better than the mode PSI value of the west.
• Both zones have the same median, 26
• Comparing the mean, the east enjoyed better air quality (25.5 compared to 28.6), with no outliers.

Hence, based on March 2011's data, quality of air in the east is better than that in the west.

Using the data from the 2 months, we are able to conclude that air quality in the eastern part of Singapore is better than the western part of the island.

Claim 2: Air Quality has worsen over the years

 The comparison is carried out by comparing the overall PSI values of the same months between 2 years (which are 5 years apart).

Comparing the data for the month of October in 2005 and 2010:

• Both Mean and Median values show that air quality in 2005 is better than that in 2010
• By comparing the median, in 2005, 15 days enjoy air quality that are 36 and below whereas in 2010, it was reduced to 10 days. 
• Moreover, in October 2010, there were 4 days with PSI value 80 and above, which in turn contributed to the higher PSI value.

 Next, comparing the data for the month of March in 2005 and 2010

• All 3 averages: Mean, Median and Mode PSI values recorded in 2005 were much hihger than than those recorded in 2010. 
• From the stem-and-leaft diagram, it was clear that more than 50% of the values are above 50. 
• Hence, air quality in 2005 is worst off than that in 2010. 

Therefore, using these 2 sets of data, we are unable to conclude that the air quality has worsened over the years.