**Data Representation**

**Classifying data, types of graphs, tables and charts and misrepresentation of data**

What are the different types of data?

All Data

Categorical

Numerical

Continuous

animals

foods

colours

Discrete

Continuous decimal scale

Exact values and often whole numbers

How would you classify these?

Use the following classifications: categorical, numerical, discrete, continuous.

The population of Parramatta.

The types of motorbikes in a parking lot.

The heights of people in a classroom.

The languages spoken at home by the students in the class.

The amount of time spent watching television.

The number of puppies in a litter.

The types of shops in a shopping centre.

The number of people attending a rock concert.

The colour of hair of the students in your class.

Line Graphs

Line graphs are used to display changes over time and are commonly used to display such data as temperature changes during the day, a company's profits or population over a period of years.

Key features of a line graph:

1. A title

2. A horizontal axis that is evenly scaled and labelled

3. A vertical axis that is evenly scaled and labelled

4. A line or smooth curve that joins successive plotted points

Column and Bar Graphs

Column and bar graphs have the following features:

1. A title

2. Labelled axes which are clearly and evenly scaled

3. Bars/columns of the same width

4. An even gap between each bar/column

5. The first bar/column begins half a unit from the axis

A divided bar graph shows a single horizontal bar, which is divided in proportion to each quantity.

Divided Bar Graphs

Key Features of a divided bar graph:

1. A title

2. The bar is divided into sections in proportion to the data

Sector graphs don't have any horizontal or vertical axes and are used to represent data that makes up parts of a whole.

Sector Graphs

Key features of a sector graph:

1. A title

2. Labelled sections and sometimes the percentages they represent

Special Types of Line Graphs - Travel, Step and Conversion graphs

Travel graphs are used to represent a journey. One axis is usually the amount of time it has taken to travel, and the other axis is the distance travelled.

Step graphs are used when a quantity increases in steps rather than gradually. e.g. westfield's carpark.

Conversion graphs are used when converting one quantity to another. e.g. currencies or degrees C to F.

Column graphs represent data in vertical columns and bar graphs represent data in horizontal bars.

How do we collect data?

There are three ways to collect data.

1. If data is collected from the whole population, it is called a

census

.

2. If data is collection from only a portion of the population, it is called a

sample

.

3. If data is gathered by watching events in their natural setting, it is called

observation

.

The ages of the students in your mathematics class.

Census, sample or observation?

The modes of transport to school by the students of a school.

The world's drinking habits.

The height of 10 friends.

The subjects most often taught by schools in NSW.

The most popular brand of soft drink in your school.

The most popular brand of soft drink in the world.

The weight of babies in the nursery at the hospital.

The number of CDs you own.

The times for swimming 50m

The most common hair colour of children in year 8.

The weight of every girl in your class.

The most popular TV show watched by your friends.

What if the sectors are unlabeled?

If the sectors are unlabeled, then we need to find out the percentage of each sector.

There are two ways to find the percentage that the sector represents.

1. We can use the angle of the sector as a fraction over 360 degrees

2. We can use the data for that sector as a fraction over the total.

How do we do this? Easy!!

1. Measure the size of the angle of each sector using a protractor.

2. Express each of the angles as a fraction of 360 degrees.

3. Simplify the fraction if possible. This is called a

proportion

.

4. Multiply the fraction by 100 to calculate the fraction as a percentage.

Finding the percentage using the angle of each sector

Finding the percentage using the data given

How do we do this? Easy!!

1. Calculate the total for the data given.

2. Express each category as a fraction over the total amount.

3. Simplify the fraction if possible. This is called a

proportion

.

4. Multiply the fraction by 100 to calculate the fraction as a percentage.

Drawing Sector Graphs

To draw sector graphs, we need to know how big to make each sector. For this, we need to calculate the angle for each sector based on the data given.

How do we do this? Easy!!

1.

Calculate the total for the data given.

2. Express each category as a fraction over the total amount.

3. Simplify the fraction if possible. This is called a

proportion

.

4. Multiply the fraction by 360 to calculate angle of the sector.

Now that we know how big we need to draw each sector, we can construct our graph.

Drawing Sector Graphs

But how? EASY!!

1. Draw a circle and mark the centre.

2. Construct a radius.

3. Draw the first angle from the radius using your protractor.

4. Measure the next angle from the last radius.

5. Continue until you have all the sectors represented.

6. Colour and label your graph.

Would a census, sample or observation be used to collect data on the following:

The most common colour car that drives past RPCS.

The number of Kookaburras in a particular area

Primary and Secondary Data

Primary data is data collected by the user. For example, if you measured the height of each Year 8 student in the school and found the average height.

Secondary data is data collected by others. This includes web-based data sets, the media, books, scientific papers, etc. An example of this would be using a website such as "census at school" to find the average height of Year 8 students.