STA 210 Lecture Notes - Lecture 4: Standard Deviation

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~ Statistics Lecture #4 ~
Descriptive Statistics: Brief Review of Elementary Topics
o Average (Mean)
o By hand:
Add them all up and divide by how many you have.
o In Excel:
o Median
o By hand:
Have to first put your data in ascending or descending order
If there are a n odd number of data values, then there will be an unambiguous
middle to the ordered list.
This middle is the MEDIAN.
If there are an even number of data values, then there will be an unambiguous pair
of two numbers in the middle of the ordered list.
The average of those two numbers is the MEDIAN in this case.
o In Excel:
o Your Point?
o Simple average is sensitive to outlying data.
Median is typically a better measure of vague ideas of center of our data in those
o Relevant to human inferences we might make
o So Why is Mean so Common?
o Easy to compute
o Totally fine for data without extreme values
o Essential part of standard deviation
o Has mathematical properties as an estimator that are much more accessible than those of
the median
o Standard Deviation
o Most common way to describe variation in data and variation matters.
o By hand:
Subtract the mean from each observation and square the difference.
Add all those up and divide by n-1.
Take the square root.
o In Excel:
o How is this Relevant to Us Now?
o Standard deviation is also very sensitive to outliers.
o If outliers are present, therefore, it can easily mess up any human inference you make from
how spread out this number might suggest your data are.
o So Why is Standard Deviation so Common?
o Lots of data naturally have a symmetric shape if you graph them.
Some dee underlying reasons for that.
But likely no outliers in that kind of shape.
o Has mathematical role in the use of a so-called normal distribution that is really important
o Upshots?
o To increase the integrity of human inferences from statistical constructs, it helps to have:
Basic Numeracy
Competence with decimal points, rates, graphs
Basic familiarity with super simple statistical calculations
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