RPN Financial 12 manual · Chapter 13 of 16

Statistics

Enter data with Σ+, then find means, standard deviations, a fitted line, estimates, correlation and a weighted mean.

13.1Enter data with Σ+#

Statistics collect data into registers R1 to R6: R1 holds the count n, R2 the sum of x, R3 the sum of x², R4 the sum of y, R5 the sum of y² and R6 the sum of xy.

For a data point with two values, key in y, press ENTER, key in x and press Σ+ (Σ+). The display shows n, the number of points so far. For one variable, simply key in x and press Σ+. Start a new data set with fΣSST (CLEAR Σ).

y
ENTER
x
Σ+
n is shown

Entering one data point.

Register	Holds
R1	$n$ , the number of points
R2	$\sum x$
R3	$\sum x^{2}$
R4	$\sum y$
R5	$\sum y^{2}$
R6	$\sum xy$

Example 13.1

Enter four data points

Enter (x, y) = (1, 2), (2, 4), (3, 5), (4, 8), each as y, ENTER, x, Σ+.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+

13.2Find the mean and standard deviation#

\bar{x}=\frac{\sum x}{n}\qquad s_x=\sqrt{\frac{n\sum x^{2}-\left(\sum x\right)^{2}}{n(n-1)}}

The mean and the sample standard deviation (the same for y).

gx̄0 (x̄) gives the mean of x in X and the mean of y in Y. gs. (s) gives the sample standard deviation: s of x in X and s of y in Y. The mean needs one point. The standard deviation needs at least two.

Example 13.2

Mean of x and y

Enter the data, then press g, x̄.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+gx̄0

Example 13.3

Standard deviation

Enter the data, then press g, s and show four decimals.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+gs.f4

Example 13.4

No data is an error

Press g, x̄ before entering anything.
gx̄0

13.3Estimate y from x and x from y#

y=A+Bx\qquad B=\frac{n\sum xy-\sum x\sum y}{n\sum x^{2}-\left(\sum x\right)^{2}}\qquad A=\bar{y}-B\bar{x}

The least-squares line used for the estimates.

Key in an x value and press gŷ,r2 (ŷ,r) to estimate y from the fitted line. Key in a y value and press gx̂,r1 (x̂,r) to estimate x. In both cases the estimate appears in X and the correlation coefficient r in Y.

r=\frac{n\sum xy-\sum x\sum y}{\sqrt{\left(n\sum x^{2}-(\sum x)^{2}\right)\left(n\sum y^{2}-(\sum y)^{2}\right)}}

The correlation coefficient r: close to 1 or −1 means the points lie near a line.

Example 13.5

Estimate y when x is 5

Enter the data. Key in 5 and press g, ŷ,r.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+5gŷ,r2

Example 13.6

The correlation coefficient

Press x⇄y to see r, with four decimals.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+5gŷ,r2x⇄yf4

Example 13.7

Estimate x when y is 10

Key in 10 and press g, x̂,r.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+10gx̂,r1f4

13.4Weighted mean#

Enter each value as y with its weight as x (so key in the value, ENTER, the weight, Σ+). Then gx̄w6 (x̄w) gives the weighted mean of the values.

\bar{x}_w=\frac{\sum xy}{\sum x}

Example 13.8

Weighted mean of the sample data

After entering the four points, press g, x̄w.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+gx̄w6

13.5Remove or correct a data point#

To remove a point you entered by mistake, key in exactly the same y and x, and press gΣ−Σ+ (Σ−). The count goes down by one. To fix a point, remove the wrong one and then enter the right one.

Example 13.9

Remove a point

Enter four points, then remove the last one with Σ−. Recall R1 for n.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+8ENTER4gΣ−Σ+RCL1

13.6Read the sums#

Recall any statistics register with RCL: RCL 1 gives n, RCL 2 gives Σx, RCL 4 gives Σy and so on.

Example 13.10

The sum of x

After entering the data, recall R2.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+8ENTER4Σ+RCL2

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