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	29	32	34	34	34	35	35	36	37	38
41	41	41	42	44	47	47	49	51	53	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 67th percentile.

Answer 1

there are N=30 ordered observation

(a) first quartile will be 8th observations (next to N/4=30/4=7.5 )=34

third quartile will be 23rd observations( next to 3N/4=3*30/4=22.5)=49

(b) second decile will be 7th observation ( next to 2*30/10=6)=32

eighth decile will be 25th observation ( next to 8*30/10=24)=53

(c) 67th percentile will be 21st observations (next to 67*30/100)=20.1) =47

the quartiles are the three values that split a data set into four equal parts.

the deciles are the three values that split a data set into 10 equal parts.

the percentiles are the three values that split a data set into 100 equal parts.