David W. answered • 02/26/16
Tutor
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“The most common measures of central tendency are the arithmetic mean, the median and the mode.” – Wikipedia
It really, really helps us humans to view the data in sorted order or as a frequency distributionwhen we want to under central tendancy.
Here is our data in ascending order:
260, 1506, 1515, 1536, 1581, 1596, 1670, 1844, 1969, 1981
And, here is a frequency distribution(by hundreds):
1
2 x
3
4
5
6
7
8
9
10
11
12
13
14
15 xxxxx
16 x
17
18 x
19 xx
20
So, what value is at the “center” of this data.
The mean (arithmetic average) is greatly different if you consider 260 versus if you do not. It is called an “outlier.” As an example, think of the grades for a college statistics class of students who have been systematically pressed toward the “mediocre middle” (my term) by the education system with a few excellent students (who have resisted this pressure to conform) and with one “party-goer” student who often doesn’t attend class or do homework.
A mean (arithmetic average) of 1546 versus 1689 is quite different.
A median (half of observations above and half below) of 15 is quite realistic (and it indicates “central tendency,” not “spread” – we need variance or standard deviation, etc. for that).
A mode (the most-frequently occurring observation) of 15 is also good. For that college statistics class, you might have observed, “This class must be required for math majors because most of the class is math majors.”
Now, the cruise ship company might tell you that 260 was a typo or give you a good reason why more than 1000 people cancelled or failed to register for that cruise (note: that airlines sometimes fly a plane with almost no passengers). But, if you want an estimate for “How many people are usually on one of these cruises?” then this mean is a poor measure.
PLZ write your own answer to: "best average load and why."
