Let's analyze the given data for each exhibit in terms of the mean age of the artifacts and the standard deviation (SD):
- Exhibit A: Mean = 42, SD = 4.9
- Exhibit B: Mean = 96, SD = 3.7
- Exhibit C: Mean = 234, SD = 6.1
The consistency in the age of artifacts within an exhibit can be evaluated by looking at the standard deviation. A higher standard deviation indicates less consistency (more variability) in ages. To find the exhibit with the least consistency in the age of the artifacts, we compare the standard deviations:
- SD for Exhibit A: 4.9
- SD for Exhibit B: 3.7
- SD for Exhibit C: 6.1
The exhibit with the greatest standard deviation has the least consistency. Among the exhibits, the highest standard deviation is 6.1, which belongs to Exhibit C. Thus, Exhibit C has the least consistency in the age of the artifacts.
Here is the completed statement:
Exhibit [tex]$\text{C}$[/tex] shows the least consistency in the age of the artifacts in the exhibit, because its [tex]$\text{standard deviation}$[/tex] is the [tex]$\text{greatest}$[/tex].