In: Statistics and Probability
An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 39.1, and 51.48. Calculate the sample mean and sample standard deviation. Round your answers to 2 decimal places.
Sample mean =
Sample standard deviation =
Solution:
Given that,
| x | dx | dx2 | 
| 36.45 | -6.55 | 42.9025 | 
| 67.90 | 24.9 | 620.01 | 
| 38.77 | -4.23 | 17.8929 | 
| 42.18 | -0.82 | 0.6724 | 
| 26.72 | -16.28 | 265.0384 | 
| 50.77 | 7.77 | 60.3729 | 
| 39.1 | -3.9 | 15.21 | 
 x
= 301.89 | 
 dx
= 0.89 | 
 dx2
= 1022.0991 | 
a ) The sample mean is 
Mean 
 = 
 x / n
= 36.45+67.9+38.77+42.18+26.72+50.77+39.1 / 7
= 301.89 / 7
= 43.1271
Mean 
 = 43.13
b ) The sample standard is S
  S = 
 ( 
 dx2 ) - (( 
dx )2 / n ) / 1 -n )
= 
 (1022.0991 ( (- 0.89 )2 / 7 ) / 6
   = 
( 1022.0991 -0.1132 / 6 )
=
( 1021.9859 / 6 )
= 
170.331
= 13.05
The sample standard is = 13.05