The Museum of HP Calculators

Mean, Standard Deviation, Standard Error for the HP-65

This program is Copyright © 1974 by Hewlett-Packard and is used here by permission. This program was originally published in the HP-65 Standard Pac.

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Card Labels
Mean, Standard Deviation, Standard Error
Label Σ+ x̄ Std Dev. Std Err. Σ-
Key A B C D E

Overview

Given a set of data points:

{x1, x2, x3, . . . . . . ., xn}

the program calculates the mean, the standard deviation (by either of two methods) and the standard error (by either of two methods.)

Formulas

x̄ = 1/n * Σ(i=1...n)xi

Std deviation = std(x) = √[ (Σxi2 - n x̄2) / (n-1) ]

Alternate Std deviation = std'(x) = √[ (Σxi2 - n x̄2) / n ]

Standard error of mean = std error = std(x) / √n

Alternate standard error of mean = std error' = std'(x) / √n

Instructions

Step Instructions Input Data/Units Keys Output Data/Units
1 Enter Program      
2 Initialize   RTN R/S 0.00
3 Repeat 3 for each x xi.... xn A 1.... n
  (Eliminate any x values entered      
  in error - x error) x error E  
4 Compute mean(x)   B mean(x)
5 Compute Std deviation of x   C std(x)
6 and by alternate method   R/S std'(x)
7 Compute std error of the mean   D std error
8 and by alternate method    R/S std error'
9 For new case, go to 2      

Example

In a recent survey to determine the average age of the wealthiest people in the U.S., the following data were obtained:

62, 84, 47, 58, 68, 60, 62, 59, 71, 73

Of the ages given, what is the mean, standard deviation and standard error of the mean?

Initialize by pressing RTN and R/S. The calculator displays 0.00. key 62 and press A. The calculator displays 1.00. Key each additional age and press A. The calculator displays the count of the data entered.

Press B to compute the mean of 64.40. Press C to compute the standard deviation of 10.10. (Then press R/S if you want to see the alternate version.) Press D to compute the standard error of 3.19. (Then press R/S if you want to see the alternate version.)

The Program

 CODE  KEYS
   00  0
33 01  STO 1
33 02  STO 2
33 03  STO 3
   84  R/S

   23  LBL
   11  A
   33  STO
   61  + 
   02  2 
   32  f-1
   09  √x
   33  STO
   61  + 
   03  3
34 01  RCL 1
   01  1 
   61  +
33 01  STO 1
   24  RTN

   23  LBL
   12  B
34 02  RCL 2
34 01  RCL 1
   81  ÷ 
   24  RTN

   23  LBL
   13  C
34 03  RCL 3
34 02  RCL 2
34 01  RCL 1
   81  ÷
   32  f-1
   09  √x
34 01  RCL 1
   71  ×
   51  -
34 01  RCL 1
   81  ÷
   31  f
   09  √x
34 01  RCL 1
34 01  RCL 1
   01  1
   51  -
   81  ÷
   31  f
   09  √x
   71  ×
   24  RTN
35 07  g x⇔y
   84  R/S 

   23  LBL 
   14  D 
   13  C
34 01  RCL1
   31  f 
   09  √x
   81  ÷
35 07  g x⇔y
35 00  g LST X 
   81  ÷
35 07  g x⇔y
   84  R/S
35 07  g x⇔y
   24  RTN 

   23  LBL 
   15  E 
   33  STO 
   51  -
   02  2 
   32  f-1
   09  √x
   33  STO 
   51  - 
   03  3 
34 01  RCL 1
   01  1
   51  -
33 01  STO 1
   24  RTN
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP

Register Use

R1  n
R2  Σxi
R3  Σxi2

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