Reference no: EM133656473
Question 1: The data shown below contains family incomes (in thousands of dollars) for a random sample of 50 families from across Australia, surveyed in 2020 and again in 2024.
|
2020
|
2024
|
2020
|
2024
|
2020
|
2024
|
|
58
|
54
|
33
|
29
|
73
|
69
|
|
6
|
2
|
14
|
10
|
26
|
22
|
|
59
|
55
|
48
|
44
|
64
|
70
|
|
71
|
57
|
20
|
16
|
59
|
55
|
|
30
|
26
|
24
|
20
|
11
|
7
|
|
38
|
34
|
82
|
78
|
70
|
66
|
|
36
|
32
|
95
|
97
|
31
|
27
|
|
27
|
23
|
22
|
18
|
34
|
30
|
|
22
|
47
|
50
|
75
|
36
|
61
|
|
141
|
166
|
124
|
149
|
125
|
150
|
|
72
|
97
|
113
|
138
|
121
|
146
|
|
165
|
190
|
118
|
143
|
88
|
113
|
|
79
|
104
|
96
|
121
|
|
|
Find the mean, median, standard deviation, first and third quartiles, and the 96th percentile for family incomes in both years.
Question 2:
In an effort to provide more consistent customer service, the manager of a local fast-food restaurant would like to know the dispersion of customer service times in relation to their average value for the facility's drive-up window. The table below provides summary measures for the customer service times (in minutes) for a sample of 50 customers collected over the past week.
|
Count
|
50.000
|
|
Mean
|
0.873
|
|
Median
|
0.885
|
|
Standard deviation
|
0.432
|
|
Minimum
|
0.077
|
|
Maximum
|
1.608
|
|
Variance
|
0.187
|
|
Skewness
|
-0.003
|
a. Interpret the variance and standard deviation of this sample.
b. Are the empirical rules applicable in this case? If so, apply them and interpret your results. If not, explain why the empirical rules are not applicable here.
c. Explain why the mean is slightly lower than the median in this case.