The Thomas Supply Company Inc. is a distributor of gas-powered generators. As wi
ID: 3070644 • Letter: T
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 28 31 34 34 34 35 35 36 37 38 41 41 4145 46 4747 50 53 53 55 56 62 67 82 (Round your answers to 2 decimal places.) a. Determine the first and third quartiles. Q1 b. Determine the second decile and the eighth decile. c. Determine the 67th percentile.Explanation / Answer
( a )
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 28 31 34 34 34 35 35 36 37 38 41 41 41 45 46 47 47 50 53 53 55 56 62 67 82
So, the bottom half is
13 13 13 20 26 28 31 34 34 34 35 35 36 37 38
The median of these numbers is 34.
Q1 = 34
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 28 31 34 34 34 35 35 36 37 38 41 41 41 45 46 47 47 50 53 53 55 56 62 67 82
So, the upper half is
41 41 41 45 46 47 47 50 53 53 55 56 62 67 82
The median of these numbers is 50.
Q3 = 50
( b )
D2 = 29.5
D8 = 53
( C )
67TH Percentile
= (67/100 )* 30
= 20.1
So 20th value is the 67th percentile
13 13 13 20 26 28 31 34 34 34 35 35 36 37 38 41 41 41 45 46 47 47 50 53 53 55 56 62 67 82
So 20th value in the above data set is 46
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