STA 210 Lecture Notes - Lecture 4: Standard Deviation
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9 Sep 2019
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~ Statistics Lecture #4 ~
Descriptive Statistics: Brief Review of Elementary Topics
09/05/19
o Average (Mean)
o By hand:
▪ Add them all up and divide by how many you have.
o In Excel:
▪ =AVERAGE(A1:A10)
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:
▪ =MEDIAN(A1:A10)
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
cases.
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:
▪ =STDEV(A1:A10)
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