 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.

 Mean, Standard Deviation, Standard Error Label Mean(x) Std Dev. Std Err. 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

mean (x) = 1/n * (i=1...n)xi

Std deviation = std(x) = sqrt(( xi2 - n mean(x)2)/ (n-1))

Alternate Std deviation = std'(x) = sqrt(( xi2 - n mean(x)2)/ n)

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

Alternate standard error of mean = std error' = std'(x)/sqrt(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  sqrt
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  sqrt
34 01  RCL 1
71  x
51  -
34 01  RCL 1
81  ÷
31  f
09  sqrt
34 01  RCL 1
34 01  RCL 1
01  1
51  -
81  ÷
31  f
09  sqrt
71  x
24  RTN
35 07  g x<>y
84  R/S

23  LBL
14  D
13  C
34 01  RCL1
31  f
09  sqrt
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  sqrt
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 xi
R3 xi2
```