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# DATA

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by

## Yee-Ling Ng

on 18 November 2016

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#### Transcript of DATA

DATA

Mean - average of a collection of numbers or set of score.

It is found by finding the total of the scores then dividing it by the number of scores.

Mean and Averages
E.g. Find the mean of the goals scored over the soccer season : 2, 3, 4, 5, 6

= 2 + 3 + 4 + 5 + 6 = 20 = 4
5 5
Averages
In pairs - what does a Moriah student look like (in maths terms!)
- Where do they live?
- What do they eat?
- How do they dress?
- What do they study, etc.

Complete ABS - http://spotlight.abs.gov.au
A Moriah Student
A Moriah Student
What questions would we need to ask to get a better question?
How could we collect this data?
How could we present this data?
How careful would we need to be when collecting the data?
What would happen if we made a mistake?
What predictions could we make with the data?
How could we use this information?
What are averages?
Think of a sentence which uses averages.
Work: Textbook (127) and sheets
Foot
1. Collect foot sizes.
2. Fill in sheet.

Numerical data
Numerical (or measured data)
- Has a scale with equal units (e.g. cm, dollars, or minutes. Decimals would make sense).
- You can do arithmetic operation with numerical data, i.e. you can find the mean, median and range.
- You can use a column graph or line graph to represent numerical data.

- Each observation falls on one of a number of distinct categories (e.g. color preferences, year group, no. of children in the family).
-Arithmetic operations cannot be formed.
- Usually summarized by percentages.
You can use a column graph, pie graph, dot plot to represent categorical data.
Categorical Data
Schools survey sheet
Surveying
Randomness: Each member of the population has an equal and known chance of being selected.
Sample vs population: the population includes all objects of interest whereas the sample is only a portion of the population.
Numerical and categorical data.

Sheet - Sampling methods
Graphs
How can we show this information in a graph?
- What will be on the x and y axis?
When large amounts of data is collected in a survey, it is best if the data is grouped.
The data can be grouped on a tally chart or frequency table.
The groups MUST be of EQUAL WIDTH.
Column graphs can be used when data is grouped. The group is written down under each bar
.
Column Graphs
Work: Text (p.24) and Sheets
Picture Graphs
How many students voted?
How many students has got dogs? Horses?
Work: Text (p.12 and p.33)
Line Graphs
Line graphs are drawn by plotting points, then joining the points with straight lines.
They are used to record data that is changing over time.
Work: Text (p.50, 74, 105)
Divided Bar graph
The whole bar represents 24 hours
1. How many hours were spent sleeping?
2. How many hours were spent eating?
Text: p.88
Pie or Sector graphs
A pie graph is a graph drawn as a circle.
The circle is divided into parts.
It shows how something is shared or divided.
If there were 100 children surveyed, how many likes soccer? Track?
Work: text (p.85. 112, 143)
Graph investigator: www.topdrawer.aamt.edu.au/Statistics/Activities/Graph-investigator

Mode
Example:
3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are:
3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often.

Mode = 23.

The mode is simply the number which appears most often.

To find the mode, or modal value, first put the numbers in order, then count how many of each number. A number that appears most often is the mode.
Median
The Median is the "middle number" (in a sorted list of numbers).

Example: find the Median of 12, 3 and 5

Put them in order:

3, 5, 12

The middle number is 5, so the median is 5

BUT, when there are an even amount of numbers things are slightly different.

In that case we need to find the middle pair of numbers, and then find the value that would be half way between them. This is easily done by adding them together and dividing by two.
Median

When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56

In this example the middle numbers are 21 and 23.
To find the value half-way between them, add them together and divide by 2:

21 + 23 = 44
44 ÷ 2 = 22

To find the Median, place the numbers in value order and find the middle number.
Range

Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9.

So the range is 9-3 = 6.

The Range is the difference between the lowest and highest values.
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
Dot Plots
A Dot Plot is a graphical display of data using dots.
It can show many-to-one correspondence. For example
= 10 students
Years 1-9: Pets
No of pets
= 2 pets
Key
1) How may pets do Year 9 student have?
2) Which grade has the most pets? Least pets?

Surveys are used to gather information. A survey may involve the entire
population
or only a
sample.

Population -
the whole group such as every student in a school.
Sample -
a random selection taken from the population such as five students from every class in the school.
Sample Data
P. 105 & P109
Data presented in graphs and charts can be misleading.