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 32 34 34 34 35 35 36 37 38 41 41 41 4244 47 47 49 51 53 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 quartile Third b. Determine the second decile and the eighth decile. Second decile Eighth decile

Explanation / Answer

First Data arrange in ascending order,

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

Quartiles:

Qk = size of [k*(n+1)/4 ]th item

First Quartile:

Q1 = size of [1*(30+1)/4 ]th item

Q1 = size of [7.75]th item

Q1 = size of 7th item + 0.75 (size of 8th item - size of 7th item)

Q1 = 32 + 0.75 (34 - 32)

Q1 = 33.5

Third Quartile:

Q3 = size of [3*(30+1)/4 ]th item

Q3 = size of [23.25]th item

Q3 = size of 23rd item + 0.25 (size of 24th item - size of 23th item)

Q3 = 49 + 0.25 (51 - 49)

Q3 = 49.5

b) Deciles

Second deciles:

Dk = size of [k*(n+1)/10]th item

D2 = size of [2*(n+1)/10]th item

D2 = size of [2*(30+1)/10]th item

D2 = size of 6.2th item

D2 = size of 6th item + 0.20 (size of 7th - size of 6th item)

D2 = 29 + 0.20 (32 - 29)

D2 = 29.6

Eighth deciles:

Dk = size of [k*(n+1)/10]th item

D8 = size of [8*(30+1)/10]th item

D8 = size of [24.8]th item

D8 = size of 24th item + 0.80 (size of 25th - size of 24th item)

D8 = 51 + 0.80 (53 - 51)

D8 = 52.6

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