Answer :

To get the percentile

Step 1: Write the formula

[tex]\begin{gathered} P_i=(\frac{i(n+1)}{100})^{th} \\ \\ \text{where n = 13} \end{gathered}[/tex]

For the 38th percentile

[tex]P_{38}=(\frac{38(13+1)}{100})^{th}[/tex][tex]P_{38}=5.32^{th}\text{ number}[/tex]

This means that the 38th percentile is between the 5th and 6th number

[tex]\begin{gathered} P_{38}=5^{th}\text{ observation}+0.32\lbrack6^{th}-5^{th}\rbrack \\ P_{38}=41+0.32(43-41)=41.64 \\ P_{38}=41.64 \end{gathered}[/tex]

P38 = 41.64This means that approximately 38% of the data lie below 43, when the data are ranked

For the 60th percentile,

[tex]P_{60}=(\frac{60(13+1)}{100})^{th}[/tex]

[tex]P_{60}=8.4^{th\text{ }}n\nu mber[/tex]

6089

[tex]P_{}=8^{th}\text{ observation}+0.4\lbrack9^{th}-8^{th}\rbrack[/tex][tex]\begin{gathered} P_{60}=56+0.4(58-56) \\ P_{60}=56.8 \end{gathered}[/tex]

60