Question

The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices.

13 13 13 20 26 27 27 32 34 34 35 35 36 37 38 41 41 41 42 44 44 47 48 50 51 55 56 62 67 82

(Round your answers to 2 decimal places.)

Determine the first and third quartiles.

Determine the second decile and the eighth decile.

Determine the 67th Percdntile.

Answer 1

Solution:

Given that,

Arranging Observations in the ascending order

13,13,13,20,26,27,27,32,34,34,35,35,36,37,38,41,41,41,42,44,44,47,48,50,51,55,56,62,67,82

n = 30

Q₁ = ( n + 1 / 4 )^th Value of observation.

= ( 31 / 4 )^th Value of observation.

  = ( 7.75)^th Value of observation.

=  7^th observation. + 0.75 ( 8^th - 7^th )

= 27 observation + 0.75 ( 32 - 27 )

= 27 + 0.75 ( 5 )

= 27 +3.75

= 30.75

Q₁ = 30.75

Q3 = (3( n + 1 ) / 4 )^th Value of observation.

= (3* 31 / 4 )^th Value of observation.

  = ( 23.25)^th Value of observation.

=  23^th observation. + 0.25 ( 24^th - 23^th )

= 48 observation + 0.25 ( 50 - 48 )

= 48 + 0.25 ( 2 )

= 48 + 0.50

= 48.50

Q3 = 48.50

D₂ = ( 2 (n + 1) / 10 )^th Value of observation.

= ( 2*31 / 10 )^th Value of observation.

  = ( 6.2)^th Value of observation.

=  6^th observation. + 0.2 ( 7^th - 6^th )

= 27 observation + 0.2 ( 27 - 27 )

= 27 + 0.2 ( 0 )

= 27.0

D₂ = 27

D8 = ( 8 (n + 1) / 10 )^th Value of observation.

= ( 8*31 / 10 )^th Value of observation.

  = (24.8)^th Value of observation.

=  24^th observation. + 0.8 ( 25^th - 24^th )

= 50 observation + 0.8 ( 51 - 50 )

= 50 + 0.8 ( 1)

= 50 + 0.8

= 50.8

D₈ = 50.8

P₆₇ = ( 67(n + 1) / 100 )^th Value of observation.

= ( 67*31 / 100 )^th Value of observation.

  = ( 20.77)^th Value of observation.

= 20^th observation. + 0.77 ( 21^th - 20^th )

= 44 observation + 0.77 ( 44 - 44 )

= 44 + 0.77 ( 0 )

= 44

P₆₇ = 44