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An art curator records statistics about three new exhibits at her art museum. The mean age of the artifacts and the standard deviation (SD) for each exhibit are recorded in the table below.

\begin{tabular}{|c|c|c|}
\hline Exhibit A & Exhibit B & Exhibit C \\
\hline Mean [tex]$=42$[/tex] & Mean [tex]$=96$[/tex] & Mean [tex]$=234$[/tex] \\
SD [tex]$=4.9$[/tex] & SD [tex]$=3.7$[/tex] & SD [tex]$=6.1$[/tex] \\
\hline
\end{tabular}

Use the information in the table to complete the following statement.

Exhibit [tex]$\square$[/tex] shows the least consistency in the age of the artifacts in the exhibit because its [tex]$\square$[/tex] is the [tex]$\square$[/tex].



Answer :

GinnyAnswer
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].

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