The Solution:
Given the data below:
We are required to find the diameter that represents the 58th percentiles.
Step 1:
We shall re-arrange the given data in ascending order of magnitude.
[tex]\begin{gathered} 1.32,1.34,1.45,1.47,1.49,1.55,1.56,1.58,1.59,1.61,1.61,163,1.64 \\ 1.64,1.69 \end{gathered}[/tex]Step 2:
We shall calculate the 58th percentile of the given data.
Note: The diameter that represents the 58th percentile is the diameter in the 58th position when all the given diameters are ranked on a scale of 100.
[tex]\begin{gathered} (\frac{58}{100}\times N)th \\ \\ \text{Where N=15} \\ \\ (\frac{58}{100}\times15)th=(58\times0.15)th=8.7th\approx9th \end{gathered}[/tex]So, the diameter in the 9th position (after rearranging in ascending order) is 1.59.
Therefore, the correct answer is 1.59
