Answer to Question #282461 in Statistics and Probability for Charles

Question

S. The efficiency rating of 155 faculty members of a certain college was taken and is 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

1. P36

2. D5

3. Q3

Answer 1

1.

Class with (36n/100)th value of the observation in cf column

=(36⋅155/100)th value of the observation in cf column

=(55.8)th value of the observation in cf column

and it lies in the class 88-90.

P₃₆ class : 88-90

The lower boundary point of 88-90:

L=88

$P_{36}=L+\frac{(36n/100)-cf}{f}c=88+2\cdot\frac{55.8-54}{39}=88.09$

where cf is cumulative frequency,

f is frequency

2.

Class with (5n/10)th value of the observation in cf column

=(5⋅155/10)th value of the observation in cf column

=(77.5)th value of the observation in cf column

and it lies in the class 88-90.

D₅ class : 88-90

The lower boundary point of 88-90:

L=88

$D_{5}=L+\frac{(5n/10)-cf}{f}c=88+2\cdot\frac{77.5-54}{39}=89.15$

3.

Class with (3n/4)th value of the observation in cf column

=(3⋅155/4)th value of the observation in cf column

=(116.25)th value of the observation in cf column

and it lies in the class 91-93.

Q₃ class : 91-93

The lower boundary point of 91-93:

L=91

$Q_{3}=L+\frac{(3n/4)-cf}{f}c=91+2\cdot\frac{116.25-93}{36}=92.29$