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 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82(Round your answer to 2 decimal places.)a. Determine the first and third quartiles.
b. Determine the second decile and the eight decile.c. Determine the 67th percentile.

Answer 1

Answer:

Q1 = 33

Q3 = 49.75

D2 = 28.4

D8 = 29.6

67th percentile = 46.10

Step-by-step explanation:

Given the data:

13 13 13 20 26 28 30 34 34 34 35 35 36 37 38

41 41 41 45 46 47 47 49 52 54 54 56 62 67 82

The first quartile (Q1) ;

1/4(n + 1)

Where n = number of observations

n = 30

Q1 = 0.25(30 + 1) = 0.25 × 31 = 7.75

7 : corresponds to 30

0.75 : (34 - 30) × 0.75 = 4 × 0.75 = 3

30 + 3 = 33

Third quartile (Q3) :

3/4(n + 1)

Where n = number of observations

n = 30

Q3 = 0.75(30 + 1) = 0.75 × 31 = 23.25

23 : corresponds to 49

0.25 : (52 - 49) × 0.25 = 3 × 0.25 = 0.75

49 + 0.75 = 49.75

Determine the second decile and the eighth decile.

Second decile (D2)

((n+1) × (2)) / 10

= (30 + 1)(2)/10 = 6.2

6 : corresponds to 28 +

0.2 : (30 - 28 )× 0.20 = 0.4

28 + 0.4 = 28.4

Eight decile (D8)

((n+1) × (8)) / 10

= (30 + 1)(8)/10 = 24.8

24 : corresponds to 52 +

0.8 : (54 - 52 )× 0.80 = 1.6

28 + 1.6 = 29.6

67th percentile :

67% × n = 0.67 × 30 = 20.10

20: corresponds to 46

0.1 : (47 - 46) × (0.1) = 0.1

46 + 0.1 = 46.10

Answer 2

The first quartiles is 33 and third quartiles is 23.25.

The second decile is 24.8  and the eight decile is 29.6

The 67th percentile is 46.10.

Given that,

Sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38.

41 41 41 45 46 47 47 49 52 54 54 56 62 67 82

We have to determine,

Determine the first and third quartiles.

Determine the second decile and the eight decile.

Determine the 67th percentile.

According to the question,

• The first quartile (Q1) ; $\dfrac{1(n+1)}{4}$

Where n = number of observations

n = 30

Then,

$= \dfrac{1(30+1)}{4}\\\\= 0.2 \times 31\\\\= 6.2$

Then, 7 : corresponds to 30,

$(34 - 30) \times 0.75 = 4 \times 0.75 = 3\\\\30 + 3 = 33$

 And Third quartile (Q3) is; $\dfrac{3(n+1)}{4}$

Where n = number of observations

n = 30

Then,

$= \dfrac{3(30+1)}{4}\\\\= 0.75 \times 31\\\\= 23.25$

23 : corresponds to 49

$0.25 : (52 - 49) \times 0.25 = 3 \times 0.25 = 0.75\\\\49 + 0.75 = 49.75$  

• To determine the second decile and the eighth decile.

Second decile (D2) ; $\dfrac{2(n+1)}{10}$

Where n = 30

Then,

$= \dfrac{2(30+1)}{10}\\\\= 0.2 \times 31\\\\= 6.1$

6 : corresponds to 28,

$(30 - 28 ) \times 0.20 = 0.4\\\\28 + 0.4 = 28.4$

 And the Eight decile (D8); $\dfrac{8(n+1)}{10}$

Where n = 30,

Then,

$\dfrac{(30 + 1)(8)}{10} = 24.8$

24 : corresponds to 52,

$(54 - 52 ) \times 0.80 = 1.6\\\\28 + 1.6 = 29.6$

 

• To determine the 67th percentile :

67% × n = 0.67 × 30 = 20.10

20: corresponds to 46

0.1 : (47 - 46) × (0.1) = 0.1

46 + 0.1 = 46.10

The 67th percentile is 46.10

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