The Thomas Supply Company Inc. is a distributor of gas-powered generators. As wi

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 29 34 34 34 35 35 36 3738 41 41 41 42 43 46 47 4950 52 55 56 62 67 82 Click here for the Excel Data File (Round your answers to 2 decimal places.) a. Determine the first and third quartiles. First quartle Third b. Determine the second decile and the eighth decile. Second decile Eiahth decile

Explanation / Answer

Part A

First quartile

To calculate first quartile, we have to arrange data in ascending order first,

Then we have to calculate median of the data,

13,13,13,20,26,29,29,34,34,34,35,35,36,37,38,41,41,41,42,43,46,47,49,50,52,55,56,62,67,82

Median = (38 + 41)/2

               = 79/2

               = 39.5

Q1is the median of the lower half of the data.

Q1 = 34

Q3 is the median of the upper half of the data.

Q3 = 48.5

Part B

Dm = m*{(n+1)/10 }th value

      = 2*(30+1)/10

      = 6.2

To calculate second decile we will calculate sixth value and distance of 0.2 of sixth and seventh values. So,

6th observation – (7th observation – 6th observation)*0.2

29 – (29 – 29)0.2

29

Dm = m*{(n+1)/10 }th value

      = 8*(30+1)/10

      = 24.8

To calculate the eighth decile we will calculate twenty-fourth value and distance of 0.8 of twenty fourth and twenty-fifth values. So,

24th observation – (25th observation – 24th observation)*0.8

50 – ( 52 – 50 )*0.8

48.4

Part C

To calculate 67th percentile we apply this formula

i = K*n   (k = 67/100)

     30*(67/100)  

= 20.1

= 20

20th value of observation is 43

now (i + 1 )th observation

21th observation is 46

average is the percentile

(43 + 46)/2

44.5

13,13,13,20,26,29,29,34,34,34,35,35,36,37,38,41,41,41,42,43,46,47,49,50,52,55,56,62,67,82

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