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	26	29	31	34	34	35	35	36	37	38
41	41	41	42	43	46	47	48	49	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

Number of observations = 30

(a) First Quartile is the median of lower half of the data

Lower half data =

13

13

13

20

26

26

29

31

34

34

35

35

36

37

38

Hence first quartile = 31

Third Quartile is the median of upper half of the data

Upper half data =

41

41

41

42

43

46

47

48

49

53

55

56

62

67

82

Hence, third quartile = 48

(b) Deciles are the value that divide the data into 10 equal parts

Total number of data points = n = 30

Decile k = k(n+1)/10 th observation

2nd Decile = 2(30+1)/10 = 6.2th observation
6.2th observation = 6th observation + 0.20*(7th observation - 6th observation) = 26 + 0.2(29-26) =  26.6

8th Decile = 8(30+1)/10 = 24.8th observation
6.2th observation = 24th observation + 0.80*(25th observation - 24th observation) = 49 + 0.8(53-49) =  52.2

(c) 67th percentile = 0.67 * 30 = 20th observation = 43