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Tuesday, March 14, 2006 

Averages And Probability

Due to the speed inwhich we were taught this lesson... and the pie distracting me ;) there may be some things I might have missed, so here it goes...

Today we learned some tricks for the TI-83's and it had to do with averages and probability (thus the name) so I'll try to recreate them as best as I can.

First we were given a list of 6 weights of potatoe sacks from 2 different farmers (6 each)

Farmer 1Farmer 2
4940
5160
4845
5255
4735
5365

To enter the numbers press:
[stat]->[enter]-> enter the data in the respective lists -> [2nd]->[mode]

When the numbers have been entered in the lists and all is complete we now can change the information into 1-Variable Statistics by pressing:
[stat]->[>](calc)->[1](1-var Stats)->[2nd]->[1](L1)->[enter]

The screen now displays the following info:
X=50 (average of list 1)
ƩX=300 (sum of all numbers on list)
ƩX2=15028 (all the numbers on the list squared then added up)
SX=2.3664... (sample deviation)
őX=2.16024... (standard deviation)
n=6 (number of numbers on list)
minX=47 (minimum)
Q1=48 (inbetween minimum and middle)
med=50 (middle)
Q3=52 (inbetween middlde and maximum)
maxX=53 (maximum)

Pressing the same keys as before but replacing 2 for 1 like so:
[stat]->[>](calc)->[1](1-var Stats)->[2nd]->[2](L2)->[enter]
will give the results above but for list 2
X=50
ƩX=300
ƩX2=15700
SX=11.83215957
őX=10.8012345
n=6
minX=35
Q1=40
med=50
Q3=60
maxX=65



Another thing we learned was how to put info into a probability graph
we used pennies as an example and thier weights.

f(frequency)Mass(g)
22.7
42.8
342.9
713.0
943.1
743.2
173.3
43.4

With this data now entered into the lists we press:
[stat]->[>]->[1]->[2nd]->[1]->[,]->[2nd]->[2]
This mulitplies the numbers together to create a result we wanted (to tell the probability of a penny of a certian weight happening)

X=3.087
ƩX=926.1
ƩX2=2863.35
SX=0.1223
őX=0.12219
n=300
minX=2.7
Q1=3
med=3.1
Q3=3.2
maxX=3.4

Hitting [stat]->[enter] will bring you to the lists and in the L3 columnat the top we will enter another list this time its the probabilities of the pennies, easily calculated by pressing: [2nd]->[2]->[/](divide)->[3][0][0] at the top of the column and the calc does the rest

To plot this as a probability graph press [2nd]->[Y=] turn on plot 1 change to the 3rd type of graph (bar graph) then change Freq to L3 by pressing [2nd][3]
then press [window] change settings to:
Xmin=2.7
Xmax=3.5
Xscl=0.1
Ymin=-0.1
Ymax=0.35
Yscl=0.05

Pressing [graph] will show the graph in a nice pretty easy to read form

To make it a Frequency graph make Freq L2 instead of L3,
Ymin=-25 and Ymax=100

And the graph will a frequency graph instead

So thats it for all we learned, and the homework was p.108 #1-9

Happy Pi Day and I'll find that coin so everybody should give up :P
Later,
Shane

Scribe Tomorrow: Corrie




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