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.

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

Singapore is a garden city with trees planted all over the island to create a green belt that 'regulates' the quality of air in the Singapore island in a 'natural' manner. However, there would be a few days in a year where the quality of the air is affected by the forest fires in the nearby countries:

Reported in the ChannelNewsAsia.com website:

http://www.channelnewsasia.com/stories/singaporelocalnews/view/1087523/1/.html

http://www.channelnewsasia.com/stories/singaporelocalnews/view/1088509/1/.html


PSI stands for 'Pollutant Standards Index'. It is an index developed by the United States Environmental Protection Agency (USEPA) to provide accurate, timely and easily understandable information about daily levels of air pollution.

Click HERE to access the 24-hour PSI readings for Singapore.

Every year, the quality of air in Singapore in months like October is badly affected by forest fires, when compared to other months (when we heard little about such instances taking place in the nearby region).

An estate agent claims that no matter how "polluted" the air is, "Air quality in the eastern part of Singapore is always better than that in the western part of the island." Therefore the price of housing properties at East Coast area is higher than those in Boon Lay.

On the other hand, residents who lived in Singapore over the past 5 years claim that the air quality has worsened over the years, especially in the month of October.

We are going to analyse the data available at the Singapore National Environment Agency (NEA) to help us find out whether the claims are justifiable.

CLAIM No. 1:

"Air quality in the eastern part of Singapore is always better than that in the western part of the island."

• We are going to make comparison the PSI values (in the east & west part of Singapore) in March 2011.
• On your own...
• Refer to the March 2011 data at HERE
• Using the PSI values in the east and PSI values in the west
• Illustrate the data using a stem-and-leaf diagram
  
• Identify the mode and median PSI value in each area
• Compute the mean PSI value in each area
• Compare the data between the eastern and the western parts of the island. What can you conclude about the quality of air between the 2 areas in the month of October?

CLAIM No. 2:  

"Air quality has worsened over the years, especially in the month of October"

• You are going to make comparison between 2 sets of data: PSI values for 2005 and 2010. 
• On your own...
• Refer to the 2005 and 2011 March data at HERE
• Using the overall PSI values for both years
• Illustrate the data using a stem-and-leaf diagram 
• Identify the mode and median PSI value for each year
• Compute the mean PSI value for each year
• Compare the data between 2 years. What can you conclude about the quality of air between the 2 years in the month of March? 

Instructions to complete the work

• Complete the tasks in the Maths notebook
• Post your consclusions for both claims under comments.
• It should look something like this...
• Claim 1: I (agree/disagree) that the quality of the air in the east is better than the western part of the Singapore island because... {Then you use the data to compare and conclude}
• Claim 2: I (agree/disagree) that the air in Singapore has become worse over the years because... {Then you use the data to compare and conclude}

Preparation for Lesson on 14 April 2011

We are going to learn 2 new graphical representations:
(1) Stem-and-Leaf Diagrams
(2) Dot Diagrams

For Stem-and-Leaf Diagrams

• Video Lessons
• Introduction
• Example 1
• Example 2
• Example 3
• A Quiz has been set for you to check your understanding (You are given a 2nd try upon completion of the quiz)

For Dot Diagrams

• Dot Diagrams and Examples 1 & 2
• Example 3
• Example 4