Interpreting Scatter Graphs

Relationships.

Scatter Graphs are an effective quick way of seeing if two variables (measures) have an effect upon each other.

e.g.  I think that the taller you are the heavier you will tend to be.  We can see if this relationship is evident if we take the measures of say 100 people and graph them.

Here are the results for the students in a class.  You can see that each person is represented by a cross (normally we use dots).  The tallest person is also the heaviest.


Line of Best Fit - can you see that there could be a straight line drawn into the graph over the points.  How closely can you see

Scatter Plot Intro

Bivariate Data 1.11 (aka 91036) Internal Three Credits

This counts for numeracy and literacy.  

For this we are going to compare numbers with numbers in a scatterplot (aka scatter graph).  We want for there to be a relationship (this is when the dots form a line).

We start with a question, draw the graph (and stats), write some sentences on what we see and write a conclusion.  This follows the PPDAC idea from the last topic.

Key Words...
Outlier - a dot (representing a person/car/country) that sits outside the line of best fit.
Line of Best Fit - a line best drawn between the dots.  You can hand draw this on.
Tightness - how closely to the line of best fit the dots are.

Intro to Achievement Standard Stats

Change in Course.

This marks the point of the year where we are departing from our numeracy (portfolio) standards of Number, Measurement and Statistics.  I will still be accumulating more evidence from you in these areas but not setting specific work for them.  

The standards that I'm aiming to do over the remainder of the year are...

Box n Whisker (aka Box Plot)

1.  91035 Multivariate Data (internal) worth 4 credits.  This is based on box and whisker graphs (see the picture) and goes through the same PPDAC system (setting a context, collecting data, drawing stem n leaf graphs, drawing dot plots + box n whisker, calculating statistics, making observations and writing a conclusion).   This is a Level One Standard 

Scatter Plot Graph

2.  91036 Bivariate Data (internal) worth 3 credits.  This is based on scatter graphs.  But goes through the same as multivariate... PPDAC system (setting a context, collecting data, drawing stem n leaf graphs, drawing dot plots + scatter graph, calculating statistics, making observations and writing a conclusion).   This too is a Level One Standard 

These level one standards I hope we have some 'merit' grades from our class.  I will teach these topics to that upper level.

example of a mathematical network.  

3.  91260 Networks (internal) worth 2 credits.  This is a unique level two maths paper as it's not based upon any prior knowledge (basically networks is about moving across a map).  For this standard you will learn from scratch.  The credits will count for 2015 and next year level two.  This is the least challenging of the level two standards and is not an indication of the challenge in level two maths.  If you want to do level two maths you will need to do full Achievement Standard level one first.  

Depending on the classes success here will determine if we attempt a level one or level two internal probably standard.  I will indicate this to you well in advance.  Potentially another 2/3 credits.

PPDAC

Statistical Inquiry Cycle
A very common thing for all people to know is how to compare groups.  If I said which fish is bigger, snapper from Waihi or snapper from Whitianga?  I would expect you to approach the problem in a systematic way.  

We call this the "Statistical Inquiry Cycle" and it's summed up in the acronym PPDAC [you absolutely must learn this].  It is a way of approaching the answer correctly.  

In statistics there rarely is the right answer.  Say if we said the that average year 9 at Waihi College weighed 53.4kg.  It would be very unlikely that the a randomly selected student would actually weigh 53.4kg.  

PPDAC stands for...

• P roblem
• P lan
• D ata
• A nalysis
• C onclusion

Here is the summary poster that shows how PPDAC is a cycle that repeats upon itself.  It was invented by Auckland University Statistics Department and is the cornerstone of NCEA Stats - you can get about 50 NCEA credits directly from being good at PPDAC.

Kiwi Fruit Harvest

Waihi College Kiwi Fruit Harvest

The school's orchard is nearly ready for harvesting.  The school has 3 hectares of commercial crop of kiwi fruit.

Kiwifruit is produced for two main markets - export (these are finest grade kiwifruit) and the local supermarkets (these are the over/under sized or unusually shaped or marked kiwifruit).

Today we're going to measure out our sample from the orchard.

I want you to have the length width height (all to nearest cm) and weight (nearest gm) measured.

We'll have a database formed for recording this information.

This we'll use to do some statistics and graphs in our investigation.

We will be looking to see if there is a relationship between the height and the weight of kiwifruit here at Waihi College.

PPDAC

Plan - how can we gather a 'fair' sample of fruit?  What are we measuring and how are we measuring it?  What units are we going to use?  Are we rounding or making any judgement calls (e.g. a fruit with a hole in it?  The measuring is evidence for the portfolio on measurement.  

Data - we will record this on a spread sheet in class.

Analysis - we will use a scatterplot to show our data.  We will make statements about what we see.

Conclusion - there maybe a relationship (maybe not).  If there is - is that relationship positive/negative, strong?  Can we make a logic statement about what happens with length and weight?

The First Graphs

First Up Graphs

The two most common graphs (these are acceptable for the numeracy standard 26626) are back to back stem and leaf graphs.  These show the numbers/data for two categories.

The trick here is to know how to read the numbers,  Can you see where the before number is 82 beats per min?

The benefits of the back to back stem and leaf graph is that you can easily see the spread of the data and make an quick comment.  "the pulse rates are generally lower (smaller numbers) in the before category.

You can also quickly find the highest, lowest, median numbers (and the quartiles).







The second most important graph to do is our dot plot graph.  These look like.

Contexts

Getting the Context Right

You need to have for this numeracy unit standard (26627) is a real context.  E.g. We can't just hand in a page on mobile phone prices - unless this has a real context.

E.g. the school ball in July is coming up for you guys - this is a real context that we can do some statistics on.

When you are doing your work you have to include a decent descriptor of the context.  Why is it real for you to be working on?


We begin our statistical investigations with a common question.  This needs to have the right wording...

"I wonder if boys spend less on mobile phones than girls at Waihi College in year 11"  The bits underlined are complusory - the I wonder if and the specific context of where the data comes from.