Question

Given the following data find the diameter that represents the 24th percentile

Answer 1

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

`N=15`

Let us arrange the data in ascending order as shown below

`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`

Let us arrange according to percentile as shown below

The 24th percentile is between the 20th and 25th percentile shown above

That is

`\begin{gathered} 24th-percentile(range)=1.406-to-1.44 \\ So, \\ (1.44-1.406)/(5)=(0.034)/(5)=0.0068 \\ 24th-percentile=1.406+4(0.0068) \\ =1.4332 \\ \approx1.43 \end{gathered}`

Hence, the 24th percentile is 1.43