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Two groups of students were asked to make 10 measurements of the pH of a solution (with a known pH of 8.0). The resulting data is shown in the table below.

The respective coefficients of variation show that Group 2 was more precise in their pH measurements compared with the data obtained by Group 1; however, their estimation of the solution's pH was quite poor with a % accuracy of 107.4%. In contrast, Group 1 was 100% accurate in their estimation of the pH, but their measurements were highly variable. Consequently, while Group 2 was very precise, in contrast Group 1 was highly accurate but did not know it due to the inherent variation in their data (see Figure 3.1)!

Table 3.1 Estimation of pH.

Observation	Group 1	Group 2
1	6.0	8.4
2	8.7	8.6
3	9.2	8.7
4	10.0	8.9
5	6.5	8.8
6	7.5	8.5
7	9.7	8.3
8	8.8	8.4
9	6.5	8.4
10	7.1	8.9
Mean	8.0	8.59
St dev	1.453	0.223
Coefficient of variation (%)	18.2	2.6
% Accuracy	100.0	107.4

Figure 3.1 Estimation of pH: precision and accuracy. Summary of data from Table 3.1. Group A (open bar) pH = 8.0 ± 1.453 (mean ± St. dev). Group B (shaded bar) pH = 8.59 ± 0.223. Closed circles indicate raw data values for each group.

So, you can have precision without accuracy, but you will never know how accurate you are without precision.