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The corporate headquarters of Bank, an online banking company, is located in downtown Philadelphia. The director of human resources is making a study of the time it takes employees to get to work. The city is planning to offer incentives to each downtown employer if they will encourage their employees to use public transportation. Below is a listing of the time to get to work this morning according to whether the employee used public transportation or drove a car.
Public Transportation
23 25 25 30 31 31 32 33 35 38 37 42
Private
32 32 33 34 37 37 38 38 38 39 40 44
a. Find the median and the first and third quartiles for the time it took employees using public transportation. Develop a box plot for the information.
b. Find the median and the first and third quartiles for the time it took employees who drove their own vehicle. Develop a box plot for the information.
c. Compare the times of the two groups.

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Answer:

Public :

Q1 = 27.5

Q2 = 31.5

Q3 = 36

Private:

Q1 = 33.5

Q2 = 37.5

Q3 = 38.5

Step-by-step explanation:

Given the data:

Public Transportation

23 25 25 30 31 31 32 33 35 38 37 42 ;

Rearranged data :

23, 25, 25, 30, 31, 31, 32, 33, 35, 37, 38, 42

Median :

1/2(n+1)th term

n = sample size = 12

1/2(13)th term = 6.5th term

(6th + 7th)/ 2

(31 + 32) / 2 = 31.5

1st quartile :

1/4(n + 1)th term

1/4(13) th term.

Q1 = 27.5

3rd quartile :

3/4(n + 1)th term

3/4(13) th term.

Q3 = (25 + 37) / 2 = 36

Private

32 32 33 34 37 37 38 38 38 39 40 44

Rearranged data:

32, 32, 33, 34, 37, 37, 38, 38, 38, 39, 40, 44

Median :

1/2(n+1)th term

n = sample size = 12

1/2(13)th term = 6.5th term

(6th + 7th)/ 2

(37 + 38) / 2 = 37.5

1st quartile :

1/4(n + 1)th term

1/4(13) th term.

Q1 = 33.5

3rd quartile :

3/4(n + 1)th term

3/4(13) th term.

Q3  = 38.5

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