Given: A set of data showing the diameters of gold balls
To Determine: The diameter that is 24th percentile
Solution
Let us determine the position of the 24th percentile
From the given data
[tex]N=15[/tex]
Let us arrange the data in ascending order as shown below
[tex]1.34,1.38,1.39,1.41,1.47,1.48,1.50,1.51,1.54,1.54,1.55,1.62,1.67,1.68,1.69[/tex]
Let us arrange according to percentile as shown below
The 24th percentile is between the 20th and 25th percentile shown above
That is
[tex]\begin{gathered} 24th-percentile(range)=1.406-to-1.44 \\ So, \\ \frac{1.44-1.406}{5}=\frac{0.034}{5}=0.0068 \\ 24th-percentile=1.406+4(0.0068) \\ =1.4332 \\ \approx1.43 \end{gathered}[/tex]
Hence, the 24th percentile is 1.43
