This program is Copyright © 1974 by HewlettPackard and is used here by permission. This program was originally published in the HP65 Standard Pac.
This program is supplied without representation or warranty of any kind. HewlettPackard 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 
Given a set of data points:
{x_{1}, x_{2}, x_{3}, . . . . . . ., x_{n}}
the program calculates the mean, the standard deviation (by either of two methods) and the standard error (by either of two methods.)
mean (x) = 1/n * _{(i=1...n)}x_{i}
Std deviation = std(x) = sqrt(( x_{i}^{2}  n mean(x)^{2})/ (n1))
Alternate Std deviation = std'(x) = sqrt(( x_{i}^{2}  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)
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 
x_{i}.... x_{n} 
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 



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.)
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
R1 n R2 x_{i} R3 x_{i}^{2}
Go back to the
software library
Go back to
the main exhibit hall