# 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