Statistics Checklist

End of Topic
With our test coming up period one here is some final revision material.  Copy handed out in class. 

Remember for the test you'll need to have great graphing skills - straight edges with rulers, protractor (for pie graph) and a rubber to do any corrections.

Remember that you can use a calculator (it will be way easier to find the mean or the size of the angle on the pie graphs). 

Second Half Statistics Topic

The remainder of the term...
We have the election results as a focal point for the next two weeks.  An election is really a census of the entire population of the voting public (over 18 years old). 
 
The final 50% of your grade will be from a test/assessment done over one hour.  This part of the topic will be done solo (as opposed to your presentation done in pairs). 
 
The specific things that you have to be able to do are...
 

1. Put raw data (in a random order) into a stem and leaf graph.  This may be sorted or unsorted.  This may be a back to back stem and leaf graph.
2. Calculate from stem n leaf graph the measures of the centre (mean/median/mode) and the spread (range and interquartile range).
3. Use the PPDAC cycle of inquiry (know what happens when and why it happens).
4. Draw box n whisker graphs carefully in grid paper (using a ruler and correct scale/sizes). 
5. Read graphs to get information (histogram/pictograph/bar/pie/box n whisker).   

 
You are allow a calculator but not the computers for this part of the topic. 

PPDAC For The Movies

PPDAC Inquiry Summary
Now that you've had enough time to look at the database of movies from 2012 and 2013 it is important for you to consider the bigger picture idea of inquiry.

So owners of movie theatres are very interested in what movies are coming up.  The term "blockbuster" is great it means lots of people going to the movies and more $$ for the owners.  

So the initial investigation would be on assessing which year was better or if things are getting better or worse?


Remember that you presentation will need to have some slides that cover all of the PPDAC sections.

·         Problem – I will give this to you "I wonder if 2013 was a better year financial at the box office for movies".  You can make a prediction which year you think might be better just looking at the databases.   

·         Plan – I got it from a website called box office mojo.   There was way more than 100 movies but I picked the top 100 - but I choose to limit to the top 100. 

 

·        Data – Explain how you picked your sample.  What is good about the size of the sample you choose.  Also note that the data is in US dollars and rounded to the nearest million dollars. 

·        Analysis – You have to find statistics like the middle (mean/median/mode)    the spread (range and interquartile range).   You have to have some graph(s) Box n Whisker      and/or      Back to Back Stem n Leaf 

Movie PPDAC Inquiry

Sampling Avoiding Bias
There are too many movies here for us to process.  We need to pick a smaller sample so we can easily find the measures of the middle and the spread of the data.  

So how do we pick our sample?  Answer we choose randomly.  Technically random means every part of the population has an equal chance of being picked. 

Here is how to do a random sample.  Give every part of the population a number (the movies are numbers 1 to 100 already). 

Use a random number generator (10 sided dice will do this - first roll is the tens and the second roll for the ones). 

Here is a link to a random number generator online. 

Here is an online ten diced dice roller.  It is showing two dice a two and a three meaning the number 23 (on the movie database for 2013 that's the movie Evil Dead which raised $54 million dollars).


Question - Can we double count?  If the random number 23 came up again should we have Evil Dead appear in our sample twice?  Answer - No we just ignore the repeat.  It catches out students because they often forget to replace the ignored one.

We are aiming to have a big enough sample to be more accurate (too small and it can lead to bad conclusions). 

Recording our Data - It takes a long time to write out the names of the movies.  So instead to show our selection just use a highlighter to help you remember which ones you picked.  That way the only things we have to use in the calculator (or spreadsheet) are the actual numbers. 

Presentation Mark Scheme

Mark Scheme
Here is where I will be allocating marks (50% of this topic's grade).  The other 50% is on a end of topic test. 
Communicating your thinking clearly (that you've appreciated that the results will vary).
       Max mark 3.  Looking at the words on your presentation under each PPDAC heading
                            (you don't have to deviate much from the examples I've posted earlier). 
Working well with your time (avoiding any last min rush jobs).
      Max mark 3.   You've been onto the work (not just filling in time). 
Presentation (make it good).
      Max mark 2. 
Use of the PPDAC headings in your presentation (see below for more hints). 
     Max mark 1 (if you have you get this)
Mistake free working (showing working out). 
     Max mark 1 (if you show working you get this).
Teamwork (not just relying on one person). 
     Max mark 1 (if your class presentation is shared equally you get this - no just one person talking).
Thinking outside the square (big picture ideas). 
     Max mark 1 - if I can see that there. 

Total of 12. 

Hope this helps.  Presentations start on Monday. 

Movie Sub Topic

Which Year Was The Best For Movies
The next step in our statistics unit is to think about how we sample from a population.  For this I am going to supply you with a database of the top 100 grossing (that means $$$) films of two years 2012 and 2013. 

The key learning is...[the words in red are words that are vital to know/use]

1. We often have too many numbers to deal with - so we pick a smaller sample from the population.  This is called sampling.
2. Sampling can easily cause bias (remember b.s.) so we have to be fair in picking.  We can be fair by choosing randomly.
3. We still look to 'clean' any data - is there clearly an error in there.  FYI there isn't in this database I've given you. 
4. We are still focussed on the PPDAC inquiry cycle. 

To get your head in the game here are two youtube clips of the big movies of both years...

 

Here is a copy of the list that of the top 100 for each year (it goes on two pages).  I've put them into alphabetical order.  The numbers I've rounded to the nearest one hundred million dollars to put the value of these in perspective the entire NZ economy for 2013 was worth US$180 million dollars so that means a movie like Ice Age : Continental Drift was worth nearly as much as the entire NZ economy!.   

Inquiry Post Update

PPDAC On Ford v Holden
Guys - I'm away again today and tomorrow with some deputy principal jobs that I've got to have done.  I'm a bit worried about where you're at with your projects - this post is hopefully going to have you back on track...

PPDAC
A for Analysis... this is where you need to be processing your 30 numbers for the Holdens and 30 numbers for the Fords.  The main things that I need for you to have done are...

Stem and Leaf Graphs for the numbers... e.g. this graph shows some car odometers (how many kms travelled).  You can see that we're talking about 1000's of km. So the top car has 159,000km on the 'clock' and there are three cars that have all travelled 190,000's of distance.

[I would recommend rounding of big numbers to the nearest 1000]

The next calculations that you will need will be the measures of the middle. 
Mean = total/number = (159 + 162 + 168 + 173 ... + 193) / 15 = ???
Median = very middle number = 180,000km
Mode = most common (in my stem n leaf graph there is one mode) = 173,000

The next calculation is the spread
Range = highest - lowest = 193 - 159 = 34,000km

Then you need to find the upper and lower quartiles. 

note - this is worthy of your time - it is the most technical part of the PPDAC cycle.  You can find extra support examples of this further down these posts. 

The Graph(s)
You can do some histograms (bar graphs with no gaps)...

Statistics Post 9

The Range
The range is the most basic measure of the spread of data.  It shows how consistent the data is. 
When we look at the data from our dart throwing...

We can see that although Paea's average (aka mean) was the highest he was not consistent in his scores.  The range is like the measure of consistency. 

Technically the Range is = Highest minus Lowest. 

In our data Baylees Range is 18 - 4 = 14, Jordan is 17 - 3 = 14, Paea is 60 - 5 = 55, Pierce is 14 - 5 = 9, Finn is 50 - 0 = 50 and Josh was 26 - 1 = 25. 





A way of thinking about range is to think about a tank firing a shell. 



The shell will go between the longest/greatest distance (several km) to it's shortest distance (about 50m).  So the range is the difference between those two numbers (it's where the shell can land). 




Quartiles
The second major measure of the spread of the data is to know about the Upper and Lower Quartiles.  The names gives you the hint - quarters (25%). 

To find the quartiles we have to...
   Step One - Have the data all in order (lowest to highest).
   Step Two - Find the halfway (median aka middle).
   Step Three - Find the halfway of the bottom half of data (Lower Quartile).
   Step Four - Find the halfway of the top half of the data (Upper Quartile).


Quartiles lead us into a major important graph called the Box and Whisker Graph.  This is the A in PPDAC (the analysis). 

Box n Whisker Graphs allow us to compare two similar pieces of data. 

E.g. Holden Commodore vs Ford XR6's


Which Vehicle will last the longest before it's time to get rid of it?

PPDAC

P - Problem
P - Plan
D - Data
A - Analysis
C - Conclusion

What would be a good way to investigate which of these vehicles will last the longest before it's time to get rid of it?

Statistics Post 3

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.

The PPDAC Cycle