Respuesta :
Answer:
(35) The 13th percentile corresponds to an age of 40 years old.
(36) The age of 56 years old corresponds to the 73rd, 77th and 80th percentile.
(37) The ages above the 75th percentile are {56 , 56 , 57 , 57 , 61 , 61 , 65 , 66}.
(38) The ages below the 25th percentile are {28 , 35 , 38 , 40 , 41 , 41 , 42 }.
Step-by-step explanation:
Arrange the data in ascending order as follows:
28 , 35 , 38 , 40 , 41 , 41 , 42 , 43 , 43 , 43 , 44 , 45 , 47 , 47 , 48 , 50 , 50 , 50 , 53 , 54 , 54 , 56 , 56 , 56 , 57 , 57 , 61 , 61 , 65 , 66
The kth percentile is computed as:
[tex]k^{th}\ percentile=(k\%\times n)^{th}\ obs.[/tex]
(35)
Compute the percentile that corresponds to an age of 40 years old as follows:
The age of 40 years old corresponds to the 4th observation.
Compute the value of k as follows:
[tex](k\%\times 30)^{th}\ obs.=4^{th}\ obs.\\\frac{k}{100}=\frac{4}{30} \\k=13.33\\\approx13^{th}\ percentile[/tex]
Thus, the 13th percentile corresponds to an age of 40 years old.
(36)
Compute the percentile that corresponds to an age of 56 years old as follows:
The age of 56 years old corresponds to the 22nd, 23rd and 24th observation.
Compute the value of k as follows:
[tex](k\%\times 30)^{th}\ obs.=22^{nd}\ obs.\\\frac{k}{100}=\frac{22}{30} \\k=73.33\\\approx73^{th}\ percentile[/tex]
[tex](k\%\times 30)^{th}\ obs.=23^{nd}\ obs.\\\frac{k}{100}=\frac{23}{30} \\k=76.67\\\approx77^{th}\ percentile[/tex]
[tex](k\%\times 30)^{th}\ obs.=24^{th}\ obs.\\\frac{k}{100}=\frac{24}{30} \\k=80^{th}\ percentile[/tex]
Thus, the age of 56 years old corresponds to the 73rd, 77th and 80th percentile.
(37)
Compute the age corresponding the 75th percentile as follows:
[tex]75^{th}\ percentile=(75\%\times 30)^{th}\ obs.=22.5^{th}\ obs.\approx23^{rd}\ obs.[/tex]
The 23rd observation is 56.
Thus, the ages above the 75th percentile are {56 , 56 , 57 , 57 , 61 , 61 , 65 , 66}.
(38)
Compute the age corresponding the 25th percentile as follows:
[tex]25^{th}\ percentile=(25\%\times 30)^{th}\ obs.=7.5^{th}\ obs.\approx8^{th}\ obs.[/tex]
The 8th observation is 43.
Thus, the ages below the 25th percentile are {28 , 35 , 38 , 40 , 41 , 41 , 42 }.
