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?