Question

See picture inserted

Answer 1

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.

`\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}`

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.

`\begin{gathered} ((58)/(100)* N)th \\ \\ \text{Where N=15} \\ \\ ((58)/(100)*15)th=(58*0.15)th=8.7th\approx9th \end{gathered}`

So, the diameter in the 9th position (after rearranging in ascending order) is 1.59.

Therefore, the correct answer is 1.59