Math Revision Answers

Shown below

are the answers as well as the necessary working for your review.

STATISTICS (Line Graphs)

Another method of data representation is known as Line Chart or Line Graphs.

Go through the tutorial in the website.
Please click here for access to site.

You are required to know how you present your data using:

• Pie Chart
• Pictogram
• Bar Chart
• Histogram
• Line Graph/Chart

The next stage is to analyse the data.

source: http://www.bbc.co.uk/schools/gcsebitesize/maths

STATISTICS (Pie Chart and Frequency Diagrams)

The next stage after the collection of data is known as Representation of Data.

The following website shows the representation of data as Pie Chart and Frequency diagrams.

Go through the tutorial in the website and complete the given worksheet in class.

Please click here for access to site.

source: http://www.bbc.co.uk/schools/gcsebitesize/maths

STATISTICS (reading)

“ We are just statistics, born to consume resources” - Horace (65-8 BC Epistles Book 1)

When information for a statistical investigation is collected and recorded this is referred to as data.

What is a statistical investigation?

There are four processes involved in a statistical investigation

1 Collection of data (information)

Data for a statistical investigation can be collected from records, from surveys, by direct observation or by measuring or counting. Data can be collected for the whole population, which generally means all the people of things that the conclusions of a statistical investigation would apply to, or for a sample of the population.

Collection of data is the first and most important task in an investigation because unless the correct data is collected valid conclusions cannot be made.

2 Organisation and Display of Data

This involves organizing data into tables and/or displaying the data with a suitable graph so that some of the features of the data are more visible.

For the two types of data that we study in detail (categorical and numerical) there are appropriate tables and graphs.

Discrete data can be displayed by:

· Pictogram - display of information using pictures to represent frequency.

· Bar chart – display of information using bars of different lengths to represent the frequency.

This is useful for making comparison over a period of time e.g. exam results

· Pie chart – uses a circle to represent data: useful to show proportions

· Leaf-and-stem diagram – shows all the original data and therefore useful to show trend of data

· Dot diagram – each dot corresponds to one score. The frequency of a number is the number of times it occurs.

· Line graphs

A histogram may be used to display non-discrete (continuous) data

3 Calculation of Descriptive Statistics

There are some statistics that are universally used to describe a set of data.

Calculating statistics that indicate the centre of the data and the spread of the data give us a picture of the sample or population under investigation.

Reading : http://www.mste.uiuc.edu/hill/dstat/dstat.html

4 Interpretation of Statistical Data

This process involves explaining the meaning of the table, graph or descriptive statistics in terms of the variable or theory to be investigated.

Some questions that you may ask to interpret statistical data:

1. What is the title of the chart, table or graph?

2. What is the purpose of this chart, table or graph?

3. What do the labels/headings tell you?

4. What key information does the data provide?

5. What is your main conclusion about the data?

6. How were you able to interpret this chart, table or graph?

7. Who created the chart, table or graph?

8. What information does the chart, table or graph add to the given account(s) of event?

9. Does the information in this chart, table or graph support or contradict information

that you have read about this event?

Types of data

Data are individual observations of a variable. A variable is a quantity that can have a value recorded for it or to which we can assign an attribute or quality.

There are two types of variable that we commonly deal with :

Categorical variables

A quality is recorded for this type of variable.

The information collected is called categorical data.

Examples of categorical variables are:

• Colour of eyes : the categories would be blue, brown, hazel, green, violet
• Gender : Male or Female
• Marital Status : Single, Married, Separated, Divorced

Numerical variables

A numerical value is recorded for this type of variable. The information collected is called numerical data.

Examples of numerical variables are :

• The number of people in a household : the variable could take the values 1, 2, 3, 4, …

• The weight of new born babies : the variable could take any value on the number line but it is likely to be in the range of 0.5 kg to 8 kg.

• The score out of 30 on a test : the variable could take the values 0, 1, 2, …, 30

Chap 4: Saying it algebraically

Posted by Loh Kwai Yin

more about writing algebraic expressions.

http://www.quia.com/mc/319817.html

STATISTICS (real scenario challenge)

Is the road along avenue 6 too congested?
Refer to the Assessment Rubric for this activity.

Chap 16 Data Handling (Lesson 1) Worksheet 16.1 Q2

The Pie Chart below represents the traffic condition outside SST at 7.25 am on a typical morning.

(a) Find the angle of the sector representing motorcycle to the nearest degree.

(b) Find the percentage of sector representing cars, correct your answer to 3 significant figures.

courtesy of Ms LohKY

Chap 16 Data Handling (Lesson 1) Worksheet 16.1 Q1

The bar chart above shows the traffic condition outside SST at 7.05 in a typical morning.

(a) Find the number of heavy vehicles observed at 7.05 am

(b) How many more cars are there as compared to heavy vehicles at 7.05 am?

(c) What is the total number of vehicles on the road at 7.05 am?

courtesy of Ms Loh KY

STATISTICS (introduction)

STATISTICS

Definition
NOUN:
(used with a sing. verb) The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling.
(used with a pl. verb) Numerical data.

Your Task:
Identify samples of statistics or visual representation of data / information from the internet. This could be in the form of charts, tables, graphs or other creative representation. Post your link in the post-it.

Mathematics in Monopoly

Monopoly (the Game) and Probability
(based on LEAP programme: mathematics @ Science Centre Maths workshop)
source: http://en.wikipedia.org/wiki


Stage 1: Monopoly the Game - preview (please click here)

The game of Monopoly and its Rules
'Monopoly rules can sometimes be the subject of a little bit of debate, because a lot of people play with variant rules, like putting $500 and all taxes in the middle, and then awarding that money to anyone who lands on Free Parking. But that's not part of the official Monopoly rules; that's just a house rule that folks use sometime. And there's nothing wrong with that. But here's the scoop on the official Monopoly game rules.'
source: www.monopoly-man.com

Stage 2: Probability (the Maths behind the Game)
Define the following terms used in Probability and complete the 5 Questions Quiz at the end of the topic.

1. Experiment
2. Outcome
3. Event
4. P(A)

refer to Mrs Glosser's site for information





Stage 3: How Fair Is Monopoly ? (please click here)
article by Ian Steward

Your Task
Read the above article and based on your experience in playing Monopoly, state whether it is a fair game. Provide evidence based on the probability concept to support your statement.

for more article on Probabilities in the Game of Monopoly (please click here)


1-09 laying a game of Monopoly @ Science Centre Maths workshop during the 2010 LEAP: Mathematics







1-06 in action optimising winning strategies