BEC'S methods questions

[bec]

So what would I type in, do you think?
InvNorm( ?,???)

[Collin Li]

We've got:

from my final line of working, and this is in the form specified here:

= invNorm(a) is the function, where:

So,

= invNorm(0.7625) = (some number that comes out of your calculator)

Now you can proceed to solve for

[Collin Li]

An alternative approach is to plug this into your graphics calculator:

Y1 = invNorm(0.7625, X, 7)
Y2 = 50

This would be using this approach:

For a normally distributed random variable with mean and standard deviation :

= invNorm(), where

Since

Find the intersection, to find X ()

I prefer the algebraic way though.

[Mao]

oh, i see...

normPdf: don't worry about this one, MM students do not need to know the probability density function of normal distribution(s)

normCdf:
syntax

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normCdf(lower,upper,μ,σ)
where lower is the lower bound, upper is the upper bound, μ is the mean,σ is the standard deviation
e.g. to find the probability in a normal distribution with mean of 30 and sd of 7 (study score) unbounded to the left and bounded at 37 on the right:
normCdf(-∞,37,30,7)=0.841

invNorm
syntax

Code: [Select]

invNorm(area,μ,σ)
where the area is the probability in a normal distribution unbounded to the left (i.e. to negative infinity), and μ is the mean, σ is the sd
e.g. for study scores, to find the SS where I beat 75% of the state:
invNorm(0.75,30,7)=34.7

[bec]

Thanks coblin and mao, i understand now!
I also realised another way I could do it, using StatList. So for the study score example (wanting to beat 75% of the state), I would enter area=.75, = 0, =1 in the Inverse Normal function, and use that as my z-value to substitute into the formula. Your way's better though...

[Mao]

yes

the other thing is, for the standard normal distribution (μ=0,σ=1), you don't even need to enter in these values
simply just close the bracket after the main argument(s) =]

[bec]

Ok, thanks. Also, just wanted to check - can the mode be a range of values? Eg, if the portion of the pdf that was at max, was a straight horizontal line (f(x)=0.2, 0<x<1, for example) would you just say that the mode was (0,1)?

[Mao]

mmm not sure

but I'd have the tendency to go towards the centre...

mode is rarely used in statistical analysis, as cases like this (or a normal distribution with two peaks, etc) really takes away its usefulness...

so, not sure...

[Collin Li]

Yeah, you'd just say that there is "no unique mode" and state all the values where that maximum occurs, I guess.

[bec]

Hmm
I just found a question like that on a SAC from last year, the suggest solution was a range of values...I think i'd do what you suggested coblin, and just be really obvious that I understand what a mode is and emphasise that there is no "unique" mode.

[bec]

I remember a while ago I figured out a quick way to find the mean of a discrete probability distribution by using the function and sets that i had stored in StatList...I didn't write it down though and now I've forgotten it. Anyone know?

[shinny]

On a TI-84, store L1 with the X values and L2 with the Pr(X=x) values. Then head into the list menu, go to math, then sum (2nd->STAT->Right->5) and then enter L1*L2 using the 2nd-STAT->1/2 and you're done.

If you want variance (and hence SD), type L1*L2-->L3 (the arrow is using the store button), then L1*L3-->L4. After that, type sum(L3), then sum(L4)-ans^2. That's the variance, so square root what you get for the SD. It's quite tedious to do though, often it'd probly be faster doing it by hand, especially if you already have the mean =\ Prevents mistakes though I guess.

[bec]

awesome!

[Mao]

if you have the time to do all these, why don't you just use the in-built stat analyser?


on TI-83/84
go Stat->Calc->1-Var Stats

the syntax is

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1-Var Stats L1,L2
where L1 is your x values and L2 is the probability

that gives you everything you need, including mean , standard deviation , and the median Med


in TI-89, go to the Stat-list editor app, and under F4 (Calc), go to 1-var stats.
In the dialogue, "List" is your x values (list1), and "Freq" is the probability (list 2. this field is defaulted to "1"). The dialogue that pops up afterwards will give you all the info

Alternatively, you can do this in the home screen if you are using 89T, go into catalogue->F3->"onevar"
the syntax is

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tistat.onevar(list1,list2)
(simple version for our simplistic purposes)
The return value would be "done". you can then open "var-link" ("2nd" + "-"), and scroll down to the folder STATVARS. In there, there will be med_x (median), sigmax (standard deviation), sumx (expected value, which is also equal to the variable "x_bar")

[bec]

Thanks mao, that makes life a lot easier.............