Wednesday, January 29, 2014
Probability summary
(Sorry I just realized I posted this on the old 309 math blog)
Probability:
_________________________________________________________________________________
Probability: How likely an event can occur
Probability = The number of ways of achieving desired outcome
Total number of possible outcomes
Event will definitely occur = 1
Event will never occur = 0
Event will not occur = 1  probability of event occurring
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Sample space: All the possible outcomes of an experiment
S = {a, b, c ...}
Sample point = 1 of the possible outcomes
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Mutually exclusive: Both events cannot occur at the same time
Probability (A or B) = P(A) + P(B)
Independent events: Both events can occur at the same time; Outcome does not affect probability of outcome of other event
Probability (A and B) = P(A) x P(B)
_________________________________________________________________________________
Diagrams:
Probability diagrams:
Used for two independent events
Tree diagram:
Used for two or more events
Tuesday, January 28, 2014
28th Jan Recap
Math File
Use an orange/red ring file .
1. Notes Earliest at the bottom .
2. Assignments
3. Quizzes
> Repeat for each topic

Mean , Median and Mode
.They are important for their own purposes depending on the analysis you want to carry out .
. Mean is very subjective as there is an outlier that can severely affect the data .
. Median is the 50% mark , letting you see how the performance of a group is .
. Mode lets you see the most popular set of data and the trends .
Box Plot
Lower percentile  Underperforming
Upper percentile  Excelling > Able to plot data using the 2 points
. Box Plots let you see performances better for evaluation ( Better than Ogive)
 It is easier to see if the data is skewed ( Biased or shifted towards) based on where Q1 , Q2 and Q3 is
 Look at interquartile range and range to determine spread and performance as a whole .
To transfer the box plot into a cumulative frequency against value graph ,
a) Plot it vertically using Q1 , Q2 and Q3 as points
b) Plot it horizontally to see how everyone is performing .
Use an orange/red ring file .
1. Notes Earliest at the bottom .
2. Assignments
3. Quizzes
> Repeat for each topic

Mean , Median and Mode
.They are important for their own purposes depending on the analysis you want to carry out .
. Mean is very subjective as there is an outlier that can severely affect the data .
. Median is the 50% mark , letting you see how the performance of a group is .
. Mode lets you see the most popular set of data and the trends .
Box Plot
Lower percentile  Underperforming
Upper percentile  Excelling > Able to plot data using the 2 points
. Box Plots let you see performances better for evaluation ( Better than Ogive)
 It is easier to see if the data is skewed ( Biased or shifted towards) based on where Q1 , Q2 and Q3 is
 Look at interquartile range and range to determine spread and performance as a whole .
To transfer the box plot into a cumulative frequency against value graph ,
a) Plot it vertically using Q1 , Q2 and Q3 as points
b) Plot it horizontally to see how everyone is performing .
Tuesday, January 21, 2014
MONITORING OF MARKS
HI ALL,
Please check that the tabulation of marks are correct to date.
Those with R please redo the worksheet as they have either incomplete statement or wrong mathematical notation used.
All the materials must be filed in the following order:
.1 Notes
.2 Assignments
.3 Quizzes (assessments)
according to topic:
.A Financial Matters (Practical Application)  2 assignments
.B Probability  4 assignments
.C Statistics  1 assignment with 1 due in Week 5
.E Geometric Constructions  1 assignment due in Week 6
.F Equation of Circle  1 assignment in Week 7
.G Plane Geometry  1 assignment in Week 7
Should you need assistance in understanding the concept do approach me or your friends.
Key:
Marks highlighted in blue indicate excellent to outstanding quality
cell in Pink indicates no submission or work not received (reasons not stated)
R indicates work has to be resubmitted due to quality or concept
A+ outstanding work submitted
LEVEL TEST
please note the following:
TOPICS covered for Level Test (EM & AM)
ensure that you are familiar with the topics to be tested. As secondary 4 is a critical year for assessment you are expected to review past topics covered in secondary 3 and lower secondary. The regular short class quizzes administered by your ST help to review the past and new knowledge and skills.
APPARATUS and EQUIPMENTS
Ensure that you have the approved scientific calculator (with the SST sticker)
 familiarise yourself with the functions such as the STATs function
Geometrical sets (compass, protractor, rules, eraser, decent pencil)
Please check that the tabulation of marks are correct to date.
Those with R please redo the worksheet as they have either incomplete statement or wrong mathematical notation used.
All the materials must be filed in the following order:
.1 Notes
.2 Assignments
.3 Quizzes (assessments)
according to topic:
.A Financial Matters (Practical Application)  2 assignments
.B Probability  4 assignments
.C Statistics  1 assignment with 1 due in Week 5
.E Geometric Constructions  1 assignment due in Week 6
.F Equation of Circle  1 assignment in Week 7
.G Plane Geometry  1 assignment in Week 7
Should you need assistance in understanding the concept do approach me or your friends.
Marks highlighted in blue indicate excellent to outstanding quality
cell in Pink indicates no submission or work not received (reasons not stated)
R indicates work has to be resubmitted due to quality or concept
A+ outstanding work submitted
LEVEL TEST
please note the following:
TOPICS covered for Level Test (EM & AM)
ensure that you are familiar with the topics to be tested. As secondary 4 is a critical year for assessment you are expected to review past topics covered in secondary 3 and lower secondary. The regular short class quizzes administered by your ST help to review the past and new knowledge and skills.
APPARATUS and EQUIPMENTS
Ensure that you have the approved scientific calculator (with the SST sticker)
 familiarise yourself with the functions such as the STATs function
Geometrical sets (compass, protractor, rules, eraser, decent pencil)
On Your Own  For Practice, Revision & Acceleration
You would have received an email invite (at your SST account) to sign up as a member of this online portal.
For your information, the Khan Academy comes with a vast collection of video clips on almost all topics (& subtopics) in our curriculum. It also comes with quizzes that automark and therefore enables you to check your understanding and mastery of the skills. This will complement what we do in class.
Note that the quizzes are largely Multiple Choice Questions or require you to enter numerical values only. You must also keep in mind the importance of writing the working/ steps in a logical manner. Hence, practices on papers should continue.
This is a useful resource that you can use for practice, revision... and for those of you who are would like to accelerate your learning, you may pace yourself accordingly  e.g. pick a topic that would be taught this year and start to learn on your own.
Note of caution: Always check your textbook on the presentation of the mathematical notation.
For example, at secondary level, 4 x 7 should not be written as 4.7 (by inserting a dot between 4 and 7).
You may also invite your parent to sign up an account and invite him/ her as your coach.
Setup Guide for Parent:
1. Parent to set up an account
2. Student to invite Parent as Coach
3. Parent to login to monitor child's progress
4. Parent can also assign tasks for child to attempt
Wednesday, January 15, 2014
Lesson Summary (15/1/14)
Things to note :
Conditions for drawing histogram
1. Fit graph paper
2. Only use the zigzag lines if the intercepts are insignificant
3. The zigzag lines are only used for xaxis not yaxis.
if used for yaxis, drawing of the bars or curve will be affected.
4. No repeating of the zigzag lines in an axis.
PS I apologise if this is a disappointing post.
Conditions for drawing histogram
1. Fit graph paper
2. Only use the zigzag lines if the intercepts are insignificant
3. The zigzag lines are only used for xaxis not yaxis.
if used for yaxis, drawing of the bars or curve will be affected.
4. No repeating of the zigzag lines in an axis.
PS I apologise if this is a disappointing post.
01 TAXATION, GST, CESS
Last updated on 13 August 2013

Tuesday, January 14, 2014
Lesson summary 14/1/14 (Crystal)
When there are a lot of datas to analyse like the examples given, it's easier to classify the datas into groups for analysis.
The class limits are composed of the lower class limit and the upper class limit. Each class has a respective set of class limits.
When making a histogram, there should be no gaps between the bars. Therefore, the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence are calculated to be the class boundaries.
Class interval is the difference between two adjacent class boundaries.
02 STATISTICS: Class Limits, Boundaries And Intervals
READING 1:
Class Limits, Boundaries And Intervals
Class Limits
Class limits are the smallest and largest observations (data, events etc) in each class. Therefore, each class has two limits: a lower and upper.
Example:
Class  Frequency 
200 – 299  12 
300 – 399  19 
400 – 499  6 
500 – 599  2 
600 – 699  11 
700 – 799  7 
800 – 899  3 
Total Frequency  60 
Using the frequency table above, what are the lower and upper class limits for the first three classes?
For the first class, 200 – 299
The lower class limit is 200
The upper class limit is 299
For the second class, 300 – 399
The lower class limit is 300
The upper class limit is 399
For the third class, 400 – 499
The lower class limit is 400
The upper class limit is 499
Class Boundaries
Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence. Therefore, each class has an upper and lower class boundary.
Example:
Class  Frequency 
200 – 299  12 
300 – 399  19 
400 – 499  6 
500 – 599  2 
600 – 699  11 
700 – 799  7 
800 – 899  3 
Total Frequency  60 
Using the frequency table above, determine the class boundaries of the first three classes.
For the first class, 200 – 299
The lower class boundary is the midpoint between 199 and 200, that is 199.5
The upper class boundary is the midpoint between 299 and 300, that is 299.5
For the second class, 300 – 399
The lower class boundary is the midpoint between 299 and 300, that is 299.5
The upper class boundary is the midpoint between 399 and 400, that is 399.5
For the third class, 400 – 499
The lower class boundary is the midpoint between 399 and 400, that is 399.5
The upper class boundary is the midpoint between 499 and 500, that is 499.5
Class Intervals
Class interval is the difference between the upper and lower class boundaries of any class.
Example:
Class  Frequency 
200 – 299  12 
300 – 399  19 
400 – 499  6 
500 – 599  2 
600 – 699  11 
700 – 799  7 
800 – 899  3 
Total Frequency  60 
Using the table above, determine the class intervals for the first class.
For the first class, 200 – 299
The class interval = Upper class boundary – lower class boundary
Upper class boundary = 299.5
Lower class boundary = 199.5
Therefore, the class interval = 299.5 – 199.5 = 100
===========================================================
Class Interval
Comment on the following:
.1 What are the key differences between class limits, class boundaries and class intervals ?
.2 How will these differences impact the accuracy of the analysis?
===========================================================
READING 2:
class interval
Class Interval
Definition of Class Interval
While arranging large amount of data (in statistics), they are grouped into different classes to get an idea of the distribution, and the range of such class of data is called the Class Interval.
More about Class Interval
 Class intervals are generally equal in width and are mutually exclusive.
 The ends of a class interval are called class limits, and the middle of an interval is called a class mark.
 Class interval is generally used to draw histogram.
Example of Class Interval
 In the table above, heights of 20 students of a class are divided into classes with the size of each class interval being 5.
Solved Example on Class Interval
Plant scientists developed different varieties of corns that have a rich content of lysine which is a nutritious animal feed. A group of chicks were given this food to test the quality. Weight gains (in grams) of these chicks after 21 days are as recorded: 380, 321, 366, 356, 349, 337, 399, 384, 410, 329, 350, 340, 324, 396, 412, 420, 382, 318, 344, 438. By constructing a frequency distribution table for 7 classes, find the class interval in which the weight increase is maximum.
Choices:
A. 426  443
B. 335  351
C. 318  438
D. 336  353
Correct Answer: D
Solution:
Step 1: Range of the data = higher value  lower value = 438  318 = 120
Step 2: Width = Range/number of classes = 120/7 = 17.14 ˜ 18
[Round to the higher value.]
Step 3: Construct the class limits (weight gains) with width 18, so that the least and the highest values are included.
Step 4: The class limits, boundaries, tally marks and the frequency for each class (number of tally marks) are shown in the table.
Step 5:Step 6: The class interval in which the weight increase maximum is 336  353. [Frequency is more for the class 336  353.]
Comment on the following:
.1 What are the key differences between class limits, class boundaries and class intervals ?
.2 How will these differences impact the accuracy of the analysis?
Monday, January 13, 2014
HDB InfoWEB: Median Resale Prices by Town and Flat Type : Buying a Resale Flat
Authentic Learning
The Housing Development Board (HDB) in Singapore uses the median price of HDB flats in various estates as a gauge of property prices in that area.
Why is the median price used as a central tendency value instead of mean or modal values? Access the website link below to find out how statisticians decide on the most appropriate central tendency value in real life. What sort of critical thinking skills do statisticians use?
HDB InfoWEB: Median Resale Prices by Town and Flat Type : Buying a Resale Flat
Reference:
http://www.conceptstew.co.uk/PAGES/mean_or_median.html
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