Sunday, 28 July 2013

Term 3 Support Programme

Please take note of the following schedule for Support Programme in Term 3

You will be provided with handouts for review and practice
  • Term 3 Week 5: Algebra - Expansion & Factorisation
  • Term 3 Week 6: Data Handling
  • Term 3 Week 7: Percentages, Rate, Ratio & Speed
For those who are not in the above list, you are welcome to join the class if you would like to use this session as a revision session for yourself.

Term 3 (1) Level Test 2 (2) Coverage for Term 3

Dear S1-09

This is a gentle reminder of the topics that will be tested in the Level Test as well as the list of topics that we will complete in Term 3.

Note that these information were posted in the GoogleSite > Maths announcement page.

Monday, 22 July 2013

Golden Ratios



Some interesting readings:
  1. Human Body and the Golden Section
  2. The Human Heart: Application of Golden Ratio & Golden Angle 
  3. The Golden Number: Human Hand and Foot and Phi

What other interesting "ratios" have you come across?

Thursday, 18 July 2013

Relationship between my Foot & Height

Click HERE to view the class data

It has been reported that the average ratio between foot size and height is about 3.20. An adult's foot size is about 15% of his/ her total height. What do you think about yours?

Wednesday, 17 July 2013

Coverage for Term 3

1. Week 1-3 Statistics
2. Week 4    Ratio, rate & speed
3. Week 5-6 Functions & Linear Graphs
4. Week 7    Direct & inverse proportion
5. Week 8    Number sequences
6. Week 9    Basic Geometry & Polygons
7. Week 10  Geometrical Construction

International Visitor Arrivals (done by Daris Ker, Group 4)

The graph above shows the amount of visitors' Arrivals in Singapore.
The least amount of visitors was during 2003 having 6.1 million visitors.
The most amount of visitors was during 2012 having 14.4 million visitors.

mean years of schooling by yong liang no. 6 group 4

The graph shows the average years we spend studying and it clearly stats that boys spend more years schooling than girls in general . It also shows that over the years we spend more years studying , it could be possible that we need more years of schooling recently to compete with foreign workers . Because CEO's can pay foreigners less money , they will hire them if we are of equal standards , so we need to study to become better and get the better jobs.

International Visitor Arrivals (done by Shaun, Group 1)

This shows the number of visitors that arrived in Singapore from 2003 to 2012. (Measured in millions) There is a increase of visitors starting from 2003 which decreased from 2007 to 2009 before picking up at 2010

Let's Ponder (Discussion 1): Is it true that...

In preparation of the I&E Bazaar, class S1-10 conducted a survey and found that the McDonald's "Crispy Chicken Breakfast Deluxe" meal is very popular amongst the SST students. They decided to sell a similar breakfast set in that morning. 

To advertise their stall, they included the following chart in their promotional flyer. 
Their publicity gimmick was, "We are one-third of what you normally paid!"

From a consumer's point of view, what is your reaction to this publicity stunt?
Hint: Remember to elaborate your response by applying what we learnt in this topic

Remember to include your Group number before submitting the comment.

Let's Ponder (Discussion 2): Is the Change really Significant?

In the annual Town Council report, it reported the effort put in to improve the environment of the residents in the area it was in-charge of.

One aspect is the collection of refuse, which was a feedback by the residents.
The diagram shows the reported non-collections of refuse as a percentage of the total number of households in a town

Study the above diagram carefully.

1. Do you agree that the Town Council has made significant improvement? Why?

2. With reference to the visual representation, point out at least 2 areas that need improvement.
- Why do you think these 2 areas require improvement
- Suggest how to improve the representation.

Remember to include your Group number before submitting the comment.

Let's Ponder (Discussion 3): It's a "Fair" Representation?

The diagram represents the sales of socks at the bookshop in the months of April and May. In April, she sold 10 pairs of socks.

To report the improved sales to the company, the bookshop auntie represented decided to represent the sales using a 'pictogram'.

Does the above "pictogram" give a fair representation of the socks sold in these 2 months?
Give a reason to your answer.

What would you suggest to the bookshop owner to present the sales in an 'objective' manner?

Remember to include your Group number before submitting the comment.

Mean Years of Schooling (Kenneth Mah, Group 3)

This graph shows the incline from 2002 to 2012 of the mean years of schooling for the total students, male students and female students. The mean always raised except for a several years were the mean years of female students in school decreased. The mean years for male students were higher than the mean years for female students.

Tuesday, 16 July 2013

International Telephone Call Minutes (Done by Dawn Lim, Group 3)

'Question 4'
This is a bar graph showing how many international telephone call minutes every year. This bar graph shows the years from 2005 to 2012. 

International Visitor Arrivals (done by Sean Lim, Group 2)

The graph above depicts information on the amount of international visitors' Arrivals in Singapore.

The least amount of International visitors Singapore had was in 2003, the international visits dipped down into 6.1 million in 2003. The Greatest amount of international visitors Singapore had was in 2012, at 14.4 million.


Resident population- Donovan, group 1

The paragraph: 
This is a bar graph that shows you the resident population of Singapore from 1970-2012. As you can see, the population is increasing over the years but is slowing down between 2010 and 2012.

The link:

Exchange Rate (S$/US$) (end period) by Jeron

This graph would obviously show us the exchange rate from S$ to US$ is slowly decreasing over the years from 2002 to 2012. The value of S$ is rising quickly.

Residential Population ( Axel, Group 3 )

From the table, we can tell that the population has been going up since the 1970s, until 2010. From there the increase in resident population has not moved much. Singaporean do not start having children, our population may soon drop rapidly.

Exchange Rate (S$/US$) (end period)( By Benjamin, Group 4)

The graph above shows the exchange rate of singapore dollars to US dollars over the year, as seen above the exchange rate from singapore dollars to US dollars have been dropping over the years. 

Educational Attainment (done by Jia Wei, Group 4)

It shows the percentage of students with different education levels (Below Secondary, Secondary, Post-secondary(Non-Tert), Diploma & Professional qualification, University) , in 2002(orange) and 2012(green).
Less people in the past (2002) are able to get good grades and complete their studies so majority stops studying after secondary or below. The education in Singapore became better over the years and now, more people are able to complete university  studies

Trends in International Visitor Arrivals by Country of Residence, Done by: Ng Wei Jie Group 4

The "graph" shows that the number of the people coming to Singapore from the 2000 to 2011 and it shows the number by the countries, they are: Indonesia, China, Australia, India and Malaysia. The graph can also show which countries come to Singapore in a large amount. The graph can be seen as the total people visiting Singapore. It might be caused by the higher amount of foreign talent.

Visitors Arrivals(Javier Tay group 2)

This is basically a bar graph.A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulate effect (stacked bar graphs).

This bar chart basically represents the number of visitors which arrive each year, the unit being millions. The bar chart also has a graph in it to guide the bars.

Mean Years of Schooling(done by (Darie, group 2)

From this graph I could see the information about the mean years of schooling about the males,females and total number of people who lives in Singapore. The number of people who stayed in school increased over the years gradually.

International Telephone Call Minutes (Johanna Lim Ziyun, Group 1)

This graph shows the number of minutes people use to talk on the phone, from 2005 to 2012. The y axis is in millions. The people make phone calls to other countries, hence the word 'international'. 

The graph tells us that over the last few years, the number of minutes used to talk on the phone have increased tremendously. From 2005 to 2007, the increase has been gradual, not too much. In 2008, the numbers took a turn and it increased the most, of 3133 minutes. From then on, it has been increasing ever since. 

The cause of this is most probably because over the years, Singapore has expanded its business throughout the world. Singapore may have many business deals with other countries and thus, the number of minutes spent talking to foreigners overseas has increased tremendously.

Another cause of it would be because Singapore brings in foreign talent and at the same time, domestic helpers. They still need to keep in contact with their family members, so they would call them, on average thrice per month, that would mean 36 times a year. About 10% to 20% are foreigners. With the large amount, it would definitely add to the total number of minutes. 

International Telephone Call Minutes (Nikisha Tan-Mishra, Group 3) (^o^)

This graph shows the total number of minutes used in international telephone calls from 2005 to 2012, with the numbers on the y-axis being in millions. 

As you can see, there has been a gradual increase every year, other than 2011, with a drastic increase between 2009 and 2010. This means that more people make international calls over the years, probably due to our improvement in technology. 

Link: ^3^

Educational Attainment (Done by Kok Li Ying, Group 1)

Updated version:
This information that is presented is the percentage of the number of people in each level of education in 2002 and 2012.
The percentage of the students in the Below Secondary level and the Secondary decreased, while the percentage of the students in the other levels have increased.
This can infer that majority of people in 2002 stop studying when they reach about the secondary level, which results in lesser people attending university, but in 2012, more people continue to study and thus more people go up to university.

International Telephone Call Minutes (Done by Chua Shuei Ray, Group 2)

   Here is the information that I am presenting. It details the number of international telephone calls made in Singapore from 2005 to 2012. 

    As you can see, the number of international telephone calls from 2005 to 2012 has increased overall, with the year 2008 showing a huge jump from 8,457 international telephone calls from the previous year, to 10,169 international telephone calls that year. 

    This huge jump in the number of international telephone calls could be attributed to Skype launching its unlimited international call plan.  

Mean Years of Schooling (done by Kiang Jia Ming Kenneth, Group 4)

There are three lines that show the total, male and female mean ages. The three lines either increase or at rest and never decreased once(except 2005 to 2006 for females). The mean of the males is higher than the mean of females.


resident population

As it is shown above,  our residential population have been growing rapidly since 1970 until 2010 when it has increase only by 46.5 . Which means that between 2010 to 2012 there is a low birth rate in singapore.

Let's Ponder: Representation of Data - "Out-of-the-Box" way

The number of dengue infections has risen to an alarming number in 2013. NEA has been providing the public with updates, and at the same time sending alerts via the media to caution and educate the public.

Below is one of the ways that NEA presents information updates to the public.
Click HERE to access the actual visual representation.

Compare this "way" of presenting data with the "conventional" way of presenting data.
Discuss the advantages & disadvantages of presenting data in this manner.
Hint: Take different perspectives (e.g. Layman, Scientist, Doctor)

Click HERE to view the responses

"Singapore, a data driven country"

  • Why is data important to Singapore?
  • How do the different government & non-government agencies make use of such data for planning?

The Statistical Department is set up to

"...develop and maintain a national statistical system of quality, integrity and expertise. As the National Statistical Authority, the Department provides reliable, relevant and timely statistics to support Singapore’s social and economic development.

In addition to collecting, compiling and disseminating a wide range of official statistics, the Department also analyses and monitors economic and social trends, and develops and maintains national statistical databases. As the National Statistical Co-ordinator, the Department coordinates statistical activities in public agencies, provides advice on statistical subject-matters, and develops and promotes the observance of national statistical standards."


Singapore in Infographics

Interpreting Data

(A) Singapore in Figures 2013

A collection of data presented in charts & tables without elaboration/ interpretation of data

(B) Singapore Household Expenditure Survey

This report presents the main findings of the latest Household Expenditure Survey (HES). Topics covered include household consumption expenditure, households’ income, socio-economic characteristics and ownership of selected consumer durables. Changes compared to the results of previous HES conducted in 2002/03 were highlighted and detailed statistical tables presented.                            

Click HERE for the Full Report

Reading the Report... How data is interpreted
See p4-p6: Significant Increase in Spending on Food and Transport

Trends in Singapore Population - The Population Pyramid

Click at the following link to view the "Trends in Population"from Y2000 to Y2012

Here's how the visual representation looks like (image)

The comment at the end of the visual:
Singapore's population has grown older over the years. The age pyramid shows the population ageing since 2000, with the number of residents in the older age groups increasing significantly. The median age of the resident population rose from 34.0 years in 2000 to 38.4 years in 2012.

Inaugurated in January 2011, the National Population and Talent Division (NPTD) strives to achieve a sustainable, connected and integrated population for Singapore. NPTD drives the coordination and implementation of population and talent policies across Government agencies. These include policies in the areas of population augmentation, supporting marriage and parenthood, talent attraction and retention, immigration and naturalisation, integration of newcomers, and engaging overseas Singaporeans.


As a team, after viewing the animated visual representation,
discuss, what are other information can we draw out from the population pyramid that NPTD would find useful in its planning and policy implementation?

Enter your response in "Comments".
Remember to include your Group Number and Team Number in the response.

On your own...

A set of graphs are put up in the website of the Department of Statistics Singapore:

However, these graphs are not accompanied by any description.
Here are some charts that would be of the public interest:
  1. Exchange Rate (S$/US$) (end period)
  2. International Visitor Arrivals
  3. Trends in International Visitor Arrivals by Country of Residence
  4. International Telephone Call Minutes
  5. Number of Births and Deaths
  6. Mean Years of Schooling
  7. Educational Attainment
  8. Resident Population 

Your task:
  • Interpret the graph (that you are assigned to)
  • Write a short a paragraph to provide the reader an overview of the information presented. It should not be less than 20 words

Submission of Work:
  • Subject title: (e.g.) International Visitor Arrivals (done by Nimalan, Group 5)
  • The posting should have a screen capture of the graph (available in the website)
  • Key in the paragraph below the image
  • Include the URL at the end of the paragraph.
To be submitted by Tuesday 16 July 2013 (2359h)

Data Handling: Mean, Median & Mode

Measures of Central Tendency or Averages

Arithmetic Mean
  • The arithmetic mean of a set of numbers is the sum of numbers divided by the number of numbers in the set : Mean = sum of the numbers/number of numbers
  • It is most the reliable measure provided there are no extreme values in the data because all the values in the data are used in calculating.
  • Whenever the set of data contains extreme values, the median or mode would probably be more reliable because they are not influenced by extreme values.
  • The number which occurs most frequently in a set of numbers
  • It is most useful in business planning as a measure of popularity that reflects central tendency or opinion.
  • May be preferred as a measure of central tendency for describing economic, sociological and educational data.
  • The median is popular in the study of social sciences because much of the data in the social sciences contain extreme values, in the set of household incomes.
  • Median for an odd number of numbers is the middle number when the numbers are arranged in order of magnitude (i.e. ascending/descending order)
  • Median for an even number of numbers is the mean of the two middle numbers when the numbers are arranged in order of magnitude

Monday, 15 July 2013

PSI Values presented in Stem-and-Leaf Diagram

Reference: Study Notes - Constructing a Stem-and-Leaf Diagram (p20)


Because of Singapore's geographical location, we are impacted by smoke haze when there are forest fires in the region and the prevailing southwest monsoon winds blow the smoke from the fires in our direction, which usually occur in the period of May to October.

However, Singapore experiences the worst haze situation in June this year.
We are going to analyse how different the quality of air in each zone, compared to the overall quality of air in Singapore.

The Task:

(A) Gathering Data

1. Each team will be assigned to plot a stem-and-leaf diagram for the PSI value of and assigned zone (north, south, east, west), against the overall Singapore PSI value.

2. Retrieve the data from the NEA website:

3. Your reference time for everyday will be 8 am.
As the overall Singapore PSI value is presented in a range. Use the mid-point for the plotting.

(B) Organising and Presenting Data

4. The leaves on the left should be the data of the "Overall Singapore PSI value" whereas those on the right would be that of the 'zone' that your team has been assigned to.

5. Remember to include the "Key" to both sets of data.

(C) Analysing Data

6. Using the Stem-and-Leaf diagram, find the mean, median and mode of both sets of data.
Show the working to obtain the mean of each set of data clearly.

7. For each set of data, attempt to use the mean, median and mode to discuss the haze situation over the month.

8. Make a comparison of these 2 sets of data, and comment the haze situation at the zone (that your team has been assigned to) and the overall value.

Below is the chart that represents the number of hotspots in Sumatra (from 6 June to 5 July).

9. Make reference to the Overall Singapore PSI values for the month, what observations can you draw between Singapore's PSI value and the hotspots detected in Sumatra? Comment on your observations.

Other useful links


1. Complete the task on the A3 size paper provided (during lesson).
Remember to include your Group Number, Team Number & Name of members of the team in the same page.

2. Put up your solution on the noticeboard at the back of the classroom by next Monday 17 July 2013 (Wednesday)

Tuesday, 2 July 2013

Data Handling: Bar Graph vs Histogram - The Challenge

Ms Manju, the school librarian, makes use of the database management system to keep track of the loans by students.

Each month, she would present the data below in a bar graph. The bar graph shows the total number of books borrowed by category from January to May.

The Challenge
From the way the system captures the information, there are more useful information that can be extracted from the system for use.

Suggest to Ms Manju how she could make use of the data captured in the system to present a different set of information (other than the number of books borrowed by categories) using a histogram. Elaborate how this information can be used to work out with a strategy to encourage students to read more books.

As a group, present your suggested solution in the A3 paper provided. You may do 'mock up' on how the histogram looks like. Remember to label the axes of the histogram clearly.

Below the histogram, elaborate how this information can be used to work out a strategy to encourage students to read more books.

Submit your answer to Ms Loh's pigeonhole upon completion (by Tuesday 9 July 2013)*
Remember to include your Class, Group number, Name of Group Members at the bottom of the paper.
*date has been changed as we took more time for discussion

Data Handling: Bar Graph vs Histogram

Class Discussion: The similarities and differences between Bar Graph and Histogram.

Monday, 1 July 2013

Work Submission...

The following items must come in by the last period of this week:
1. Percentages - Study Notes 
2. Percentages - Homework that was done in foolscap papers
3. Topic Revision - Linear Equations
4. Study Notes for Term 1 (for checking)


  • remember to bring the Study Notes on Statistics from next lesson onwards
  • bring Homework 6A