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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:

  1. the arithmetic mean
  2. the percent error for each trial
  3. the deviation and percent deviation for each trial
  4. 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= 0.18
Dividing 0.18 by 3 (or 4-1) = 0.06
Taking the square root of 0.06= 0.245

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