The commute times (in minutes) of 30 employees are listed below.

(a) Find Qi, Q3, and the interquartile range (IQR).

(b) Find the fences and determine if there are any outliers in the sample.

20 4 45 48 52 55 56 60 63 65 67 68 6 70 74 75 77 78 79 80 81 82 8 85 87 88 90 92 95 99

Q1 = 54.25; Q3 = 82.75; IQR = 28.5; Outliers = 4, 6, 8

Step-by-step explanation:

Quartiles divide data into 4 equal parts. Q1 has 25% data below it & 75% above it, Q3 has 75% data below it & 25% data above it.

Quartile Calculation for 30 number of observations

Ascending order : 4, 6, 8, 20, 45, 48, 52, 55, 56, 60, 63, 65, 67, 68, 70, 74, 75, 77, 78, 79, 80, 81, 82, 85, 87, 88, 90, 92, 95, 99 Q1 = (N + 1) / 4th observation = [ (30 + 1) / 4 ] th obs. = (31 / 4) th = 7.75th = 7th item + 0.75 (7th - 8th item) = 52 + 0.75 (55-52) = 52 + 0.75 (3) = 52 + 2.25 = 54.25 Q3 = 3 [ (N+1) / 4] th observation = 7.75 x 3 = 23.25th item = 23rd item + 0.25 (24th - 23rd item) = 82 + 0.25 (85-82) = 82 + 0.25 (3) = 82 + 0.75 = 82.75 Interquartile range (IQR) = Q3 - Q1 = 82.75 - 54.25 = 28.5

Outliers are the observations less than Q1 - 1.5 (IQR), more than Q3 + 1.5 (IQR)

Q1 - 1.5 (IQR) = 54.25 - 1.5 (28.5) = 54.25 - 42.75 = 11.5. So, numbers less than 11.5, ie 4, 6, 8 are outliers Q3 + 1.5 (IQR) = 82.75 + 1.5 (28.5) = 82.75 + 42.75 = 125.5. There are no numbers > 125.5