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 31 33 34 34 35 35 36 37 38 41 41 41 45 45 47 47 49 51 54 55 56 62 6782 (Round your answers to 2 decimal places.) a. Determine the first and third quartiles Q1 = Q3 = b. Determine the second decile and the eighth decile. D2 = D c. Determine the 67th percentile.

Explanation / Answer

Solution:-

a. Q1 = 33 , Q3 = 49

Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

13   13   13   20   26   29   31   33   34   34   35   35   35   36   37   38   41   41   41   45   45   47   47   49   51   54   55   56   62   67   82   

So, the bottom half is

13   13   13   20   26   29   31   33   34   34   35   35   35   36   37   

The median of these numbers is 33.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

13   13   13   20   26   29   31   33   34   34   35   35   35   36   37   38   41   41   41   45   45   47   47   49   51   54   55   56   62   67   82   

So, the upper half is

41   41   41   45   45   47   47   49   51   54   55   56   62   67   82   

The median of these numbers is 49.

b. D2 = 30 D8 = 52.5

c. the 67th percentile is 45

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