Variability from 5 point Summaries (Q1) Suppose you have two lists of data, List 1 and List 2 with 100 values, and you k

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Variability from 5 point Summaries
(Q1) Suppose you have two lists of data, List 1
and List 2 with 100 values, and you know the following 5 point
summary for each list:
Data List 1 five point summary:
Data List 2 five point summary:
Which list has greater variability in the form of the
standard deviation?
Your answers could include List 1, List 2, impossible to tell,
or both. But whatever your answer is, justify
it.
(Q2) Review at least one other student's
answer to (Q1) and discuss with them whether the justification for
your answer is better than the justification for their answer (in
the case the justifications are different), or if they are the
same, whether there might be a better justification?
(Q3). Observe that when we measure or compare
values that correspond to real-world measurements, we have to add
values with the same types of unit. For example if one wants to add
together the temperatures of two containers of water, you have to
measure the temperatures using the same scale (Fahrenheit or
Centigrade for example), since it would not make sense to note that
one container is 78 degrees F and the other is 1 degree C, and
hence the combined temperature is 78 + 1 (what unit of temperature
???)
Use this principle to explain why we do not use VARIANCE to find
data values which are significantly high or significantly low. For
simplicity we will assume we have measurements from a sample where
the sample mean is denoted by x¯x¯ , and we want to determine
significantly high or low values by the computing the following
values:
x¯+s2x¯+s2 or x¯−s2x¯−s2
Why would this not work?