Statistics CommuteTime N Valid 20 Missing 0 CommuteTime Frequency Percent Valid
ID: 3504043 • Letter: S
Question
Statistics
CommuteTime
N
Valid
20
Missing
0
CommuteTime
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
10
1
5.0
5.0
5.0
16
1
5.0
5.0
10.0
20
1
5.0
5.0
15.0
21
1
5.0
5.0
20.0
23
2
10.0
10.0
30.0
24
1
5.0
5.0
35.0
25
1
5.0
5.0
40.0
32
2
10.0
10.0
50.0
37
1
5.0
5.0
55.0
42
1
5.0
5.0
60.0
56
1
5.0
5.0
65.0
63
1
5.0
5.0
70.0
68
1
5.0
5.0
75.0
72
1
5.0
5.0
80.0
80
1
5.0
5.0
85.0
85
1
5.0
5.0
90.0
91
1
5.0
5.0
95.0
104
1
5.0
5.0
100.0
Total
20
100.0
100.0
Describe the distribution of Commute Time – measures of center, measures of variation, and the shape you observe in the graph. In real-world terms, what do these measures tell us about how the commute times tend to distribute, and how could you tell? Include the relevant statistics for each one in your explanation. Which measures of center and variation are more useful for this particular sample, and why?
Statistics
CommuteTime
N
Valid
20
Missing
0
Histogram Mean = 462 Std. Dev. = 28.639 N 20 101 40 60 80 100 120 20 Commute TimeExplanation / Answer
The measures of central tendency are as follows:
Mean: 46.2
Median: 34.5
Mode: 23, 32
The measures of variability are as follows:
Standard Deviation: 28.6
Variance: 820.2
In the graph, we can observe a positively skewed distribution. In positively skewed distributions, the mean (46.2) is greater than the median (34.5), which is greater than the mode (23, 32). We can also observe that the long tail of the distribution is on the positive side of the peak.
In real world circumstances, we can say that the average time people take to commute is 46.2 minutes. However, we cannot completely rely on this measure because the distribution is skewed. It is therefore recommended that we consider the median as a measure of the center, which 34.5 minutes.
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