UNC-Chapel Hill Calculator Fundamentals Program
Department of Chemistry
An interactive educational exercise
Applications in Science: Simple Statistics
A student analyzing a sample for bromine (Br) makes four trials with the following results: 36.0, 36.3, 35.8, and 36.3. The theoretical value is 36.2
Calculate:
- the arithmetic mean
- the percent error for each trial
- the deviation and percent deviation for each trial
- the standard deviation
Arithmetic mean:
(36.0 + 36.3 + 35.8 + 36.3) / 4 = 36.1
Percent error, deviation and percent deviation for each trial
| Observed value |
Error |
Percent error |
Deviation |
Percent deviation |
| 36.0 |
-0.2 |
0.55% |
-0.1 |
-0.28% |
| 36.3 |
0.1 |
0.28% |
0.2 |
0.55% |
| 35.8 |
-0.4 |
1.1% |
-0.3 |
-0.83% |
| 36.3 |
0.1 |
0.28% |
0.2 |
0.55% |
Standard deviation
| Trial |
1 |
2 |
3 |
4 |
| Percentage of Br |
36.0 |
36.3 |
35.8 |
36.3 |
| d |
-0.1 |
0.2 |
-0.3 |
0.2 |
| d2 |
0.01 |
0.04 |
0.09 |
0.04 |
Adding up all of the d2= 0.018
Dividing 0.018 by 3 (or 4-1) = 0.06
Taking the square root of 0.06= 0.245
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Last Update: July 29, 1997
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