**HP 32S II Statistical Formulas**

**Statistics Formulas**

The 32S II can store formulas for evaluations, including formulas involving stat variables.

Covariance:

C = r × sx × sy

Root Mean Square Based on X Variable Statistics:

R = SQRT( Σx^2 ÷ n )

Z-Score Based on X Variable Statistics:

Z = (X - x-bar) ÷ sx

Accessing Stat variables:

r: [ right shift ] [ LN ] (L.R.) [ y^x ] (r)

sx: [ right shift ] [ 1/x ] (s, σ), [ √x ] (sx)

sy: [ right shift ] [ 1/x ] (s, σ), [ LN ] (sy)

Σx^2: [ right shift ] [ Σ+ ] (SUMS) [ e^x ] (x)

n: [ right shift ] [ Σ+ ] (SUMS) [ √x ] (n)

x-bar: [ right shift ] [ y^x ] (x-bar,y-bar) [ √x ] (x-bar)

Example

Data: (x, y)

(10.4, 20)

(13.5, 18)

(16.8, 15)

(19.1, 13.9)

Enter statistical data: y [ENTER] x [ Σ+ ]

Some stats:

x-bar = 14.95

y-bar = 16.725

r = -9.9503133E-1

Covariance: Solve for C

C = -10.555

Result is stored in C

Root Mean Square: Solve for R

R = 15.3089842903

Result is stored in R

Z-Score Based on X Variable Statistics: Solve for Z

X? 15, Z = 1.31382E-2

X? 17, Z = 5.38666E-1

Result is stored in Z

**Formulas vs. Programs**

If we are going to evaluate formulas (that is, solve for the variable left of the equals sign), we could also enter and use programs. The programs for the above three formulas:

Covariance:

C01 LBL C

C02 r

C03 sx

C04 ×

C05 sy

C06 ×

C07 RTN

Root Mean Square:

R01 LBL R

R02 Σx^2

R03 n

R04 ÷

R05 SQRT

R06 RTN

Z Score: (x is in the X stack)

Z01 LBL Z

Z02 x-bar

Z03 -

Z04 sx

Z05 ÷

Z06 RTN

Byte Consumption Comparison

Covariance

Formula: 12 bytes

Program: 10.5 bytes

Root Mean Square

Formula: 12 bytes

Program: 9 bytes

Z Score

Formula: 15 bytes

Program: 9 bytes

From sample set, programs are shorter than formulas. Is this true in general?

Eddie

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