RPN Advanced 42 manual · Chapter 11 of 18

Statistics

Enter data pairs with sigma-plus, then read means, deviations, sums, and fit a straight line.

11.1Enter data points#

Each data point is a pair: put y in Y and x in X, then press Σ+. After each point the display shows the number of points so far. For one-variable data, enter any y (for example 0) and the x values. Shift Σ+ removes a point you entered by mistake. The sums live in registers 11 to 16.

\bar{x}=\frac{\sum x}{n},\qquad s=\sqrt{\frac{\sum x^2-n\bar x^2}{n-1}}

Example 11.1

Add three data points

Enter (x, y) = (2, 1), (4, 2), (7, 3) as y ENTER x Σ+.
1ENTER2Σ+2ENTER4Σ+3ENTER7Σ+

Example 11.2

Remove a point

Add a point and remove it again; the count returns to zero.
2ENTER1Σ+2ENTER1⇧Σ−Σ+

11.2The STAT menu: sums, mean and deviation#

The STAT menu: Σ+, SUM, mean, weighted mean, standard deviation and FIT. The display shows: x: 0.0000 / Σ+ SUM x̄ x̄w s FIT. — The STAT menu: Σ+, SUM, mean, weighted mean, standard deviation and FIT.

Label	Result
Σ+	Adds the point (same as the key).
SUM	X = sum of x, Y = sum of y.
x̄ (MEAN)	X = mean of x, Y = mean of y.
x̄w (WMN)	Weighted mean of x using y as the weights.
s (SDEV)	X = sample standard deviation of x, Y = of y.
FIT	Opens the line-fit menu.

Example 11.3

Mean of x

Enter the three points, open STAT and press the mean key (third).
1ENTER2Σ+2ENTER4Σ+3ENTER7Σ+⇧STAT÷√x

Example 11.4

Sum of x

The SUM key (second).
1ENTER2Σ+2ENTER4Σ+3ENTER7Σ+⇧STAT÷1/x

Example 11.5

Standard deviation of x

The s key (fifth).
1ENTER2Σ+2ENTER4Σ+3ENTER7Σ+⇧STAT÷LN

Example 11.6

Weighted mean

The fourth key.
1ENTER2Σ+2ENTER4Σ+3ENTER7Σ+⇧STAT÷LOG

11.3Fit a straight line and forecast#

FIT (sixth key of STAT) opens the line-fit menu: FCX, FCY, SLP, YIN and r. They use the least-squares line $y=mx+b$ .

m=\frac{n\sum xy-\sum x\sum y}{n\sum x^{2}-(\sum x)^{2}},\qquad b=\bar y-m\bar x

The FIT menu: forecast x, forecast y, slope, intercept and correlation. The display shows: x: 0.0000 / FCX FCY SLP YIN r . — The FIT menu: forecast x, forecast y, slope, intercept and correlation.

Example 11.7

Slope of a perfect line

Points (1,3), (2,5), (3,7) lie on y = 2x + 1. Open STAT, FIT, SLP (third).
3ENTER1Σ+5ENTER2Σ+7ENTER3Σ+⇧STAT÷XEQ√x

Example 11.8

Intercept of the line

YIN is the fourth key.
3ENTER1Σ+5ENTER2Σ+7ENTER3Σ+⇧STAT÷XEQLOG

Example 11.9

Correlation

The r key is the fifth.
3ENTER1Σ+5ENTER2Σ+7ENTER3Σ+⇧STAT÷XEQLN

Example 11.10

Forecast y at x = 10

Type 10 and press FCY (second key).
3ENTER1Σ+5ENTER2Σ+7ENTER3Σ+⇧STAT÷XEQ101/x

Example 11.11

Forecast x for y = 9

Type 9 and press FCX (first key).
3ENTER1Σ+5ENTER2Σ+7ENTER3Σ+⇧STAT÷XEQ9Σ+

11.4Clear the statistics#

Example 11.12

Clear the sums

Add a point, open CLEAR and press CLΣ, then look at register 16 (the count).
2ENTER1Σ+⇧CLEAR←Σ+EXITRCL16

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