HP -11C Owner's Handbook Manual page 32

60 Section 3: Numeric Functions
Mean
The (] function computes the artithmetic mean (average) of the x
and y statistics accumulated in registers R, and R;, respectively.
When you press (9 ][X]:
1. The contents of the stack registers lift in the same way as
when you press [RCL][£+], as described on page 57.
2. The mean of the x values (x) is calculated using the statistics
accumulated in R,(Xx) and Ro(n). The mean of the y values
(¥) is calculated using the data accumulated in registers
R,(Zy) and Ro(n). The formulas used are shown below.
=. 2% -_ =
xy=—— j=
n n
3. The values for x and ¥ are placed in the X- and Y-registers of
the stack.
Example. From the five year statistical data you accumulated
(and corrected) in the previous example, calculate the average coal
production and electrical output for the entire period.
Keystrokes Display
ra
6.1352
Average electrical output
(average of X-register
inputs) for the five-year
period.
Average coal production
(average Y-register
inputs) for the five-year
period.
xzy 1.8316
sr
Section 3: Numeric Functions 61
The illustration below shows what happens in the stack when you
execute [] (assumes stack disabled, as it would be following a
operation):
lost
te CE
ze~l?l-,]
ve |< ba
xe De}
lost
Retain the preceding statistics in your HP-11C for use in the next
example.
Standard Deviation
Pressing [9] [s] computes the standard deviation (a measure of
dispersion around the mean) of the accumulated statistics data.
The formulas used by the HP-11C to compute s,, the standard
deviation of the accumulated x values, and s,, the standard
deviation of the accumulated y values are:
ge nx? — (Sx)?
* n(n—1) 7
n3y? ~ (Sy)?
n(n-1)
These formulas give the best estimates of the population standard
deviations from the sample data. Consequently, the standard
deviation given by these formulas is termed by convention the
sample standard deviation. When you press [9 ][s}:
1. The contents of the stack registers are lifted in the same way
as they are when you press [Ri +], as described on page
57.
2. The standard deviation of the x values (s,) is calculated
using the data accumulated in registers Rp (x2), R, (Ex), and
Ro (n) according to the formula shown above. The resultant
value for s, is placed in the X-register.