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	28	32	33	34	34	35	35	36	37	38
41	41	41	42	43	45	47	49	50	51	55	56	62	67	82

(Round your answers to 2 decimal places.)

1. Determine the first and third quartiles.
2. Determine the second decile and the eighth decile.
3. Determine the 67^th percentile.

Answer 1

a.

We arrange the data in ascending order as :

Now, we compute First quartie Q₁ and third quartile Q₃ as :

b.

Position of Second decile = (2/10)*(n+1) =(2/10)*(20+1) = 4.2

Second decile = 4th value + ( 4.2 - 4)*(5th value - 4th value) = 20 + ( 0.2 ) * ( 26 - 20 ) = 21.2

Position of eighth decile = (8/10)*(n+1) =(8/10)*(20+1) = 16.8

Eighth decile = 16th value + ( 16.8 - 16)*(17th value - 16th value) = 41 + ( 0.8 ) * (41 - 41 ) = 41

c.

Position of 67th Percentile= (67/100)*(n+1) =(67/100)*(20+1) = 14.07

67th Percentile = 14th value + ( 14.07 - 14)*(15th value - 14th value) = 37 + ( 0.07 ) * ( 38 - 37 ) = 37.07