The efficacy of rating of 155 faculty members of a certain college was taken and shown below.
Classes f
73-75 2
76-78 6
79-81 12
82-84 16
85-87 18
88-90 39
91-93 36
94-96 21
97-99 5
Determine the value of the following:
1. P36
2. D5
3. Q3
1.
"P_{36}" class:
Class with "(\\dfrac{36n }{100})^{th}" value of the observation in "cf" column
"(\\dfrac{36(155) }{100})^{th}" value "=(55.8)^{th}" value
It lies in the class "88-90"
"P_{36}" class: "87.5-90.5"
The lower boundary point of "87.5-90.5" is "87.5."
"L=" lower boundary point of median class"=87.5"
"P_{36}=L+\\dfrac{\\dfrac{36n}{100}-cf}{f}\\cdot c=87.5+\\dfrac{55.8-54}{39}\\cdot 3""=87.6385"
2.
"D_5" class:
Class with "(\\dfrac{5n }{10})^{th}" value of the observation in "cf" column
"(\\dfrac{5(155) }{10})^{th}" value "=(77.5)^{th}" value
It lies in the class "88-90"
"D_5" class: "87.5-90.5"
The lower boundary point of "87.5-90.5" is "87.5."
"L=" lower boundary point of median class"=87.5"
"D_5=L+\\dfrac{\\dfrac{5n}{10}-cf}{f}\\cdot c=87.5+\\dfrac{77.5-54}{39}\\cdot 3""=89.3077"
3.
"Q_3" class:
Class with "(\\dfrac{3n }{4})^{th}" value of the observation in "cf" column
"(\\dfrac{3(155) }{4})^{th}" value "=(166.25)^{th}" value
It lies in the class "91-93"
"Q_3" class: "90.5-93.5"
The lower boundary point of "90.5-93.5" is "90.5."
"L=" lower boundary point of median class"=90.5"
"=92.4375"
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