The document discusses standard deviation and how to calculate it in Python. It begins by reviewing the arithmetic mean and defining standard deviation as a measure of how spread out numbers are from the average value. It then provides the formula for calculating standard deviation. The remainder of the document demonstrates how to write Python code to calculate standard deviation for a sample list of numbers by first finding the average, then calculating the squared distance from the average for each value and averaging those distances, and finally taking the square root of the result.

1. Computer Science 151
An introduction to the art of
computing
Standard Deviation Lecture
Rudy Martinez

2. Arithmetic Mean formalized
• Remember Arithmetic Mean
• A measure of the most typical value in a set.
• 𝑥 usually denotes the mean
• More formally:
• 𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠, 𝑥, 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟
𝑥 =
𝑥
𝑁
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3. Standard Deviation
• The 𝑥 is the most likely value
as denoted by the largest area
under the curve.
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4. Standard Deviation
• For a given data set, the standard deviation measures how spread
out numbers are from an average value ( 𝑥).
𝑠 =
𝑥− 𝑥 2
𝑛−1
• As you can see you are taking the distance of each point from the
average value.
• A note, if you have the whole list of numbers and not a random
selection then n-1 becomes n!
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5. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
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6. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
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7. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
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8. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
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9. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
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10. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
• Then iterate over the list of values subtracting the mean from the
item in the list, and write that to a list.
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11. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
• Then iterate over the list of values subtracting the mean from the
item in the list, and write that to a list.
xbarValues = [ ]
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12. How do we do this in Python?
• Saw we have a list of values
myList = [65, 45, 78, 92, 27]
• First we need to calculate the arithmetic mean and store that.
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
• Then iterate over the list of values subtracting the mean from the item in
the list, and write that to a list.
xbarValues = [ ]
for i in range(0, len(myList), 1):
xbarValues[i] = math.pow((myList[i] – xbar),2)
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13. How do we do this in Python?
myList = [65, 45, 78, 92, 27]
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
xbarValues = [ ]
for i in range(0, len(myList), 1):
xbarValues[i] = math.pow((myList[i] – xbar),2)
• Sum the list and divide by the length of the list, then take the square root.
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14. How do we do this in Python?
myList = [65, 45, 78, 92, 27]
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
xbarValues = [ ]
for i in range(0, len(myList), 1):
xbarValues[i] = math.pow((myList[i] – xbar),2)
• Sum the list and divide by the length of the list, then take the square root.
xbarSum = 0.0
for i in range(0, len(xbarValues)1):
xbarSum += xbarValues[i]
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15. How do we do this in Python?
myList = [65, 45, 78, 92, 27]
sum = 0.0
for i in range(0, len(myList), 1):
sum += myList[i]
xbar = sum/len(myList)
xbarValues = [ ]
for i in range(0, len(myList), 1):
xbarValues[i] = math.pow((myList[i] – xbar),2)
• Sum the list and divide by the length of the list, then take the square root.
xbarSum = 0.0
for i in range(0, len(xbarValues)1):
xbarSum += xbarValues[i]
s = math.sqrt(xbarSum/len(xbarValues))
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16. How do we apply this to our data?
• Recall we have a both a clean set of data values in Homework2.csv
• Year, Tmax, Tmin
• We also have the average per year in averagedata.csv
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17. Final Exam/Project
• You should declare by email which one you would like to do.
• Email rudym@cs.unm.edu
• Subject CS151sp19 Final
• Body should contain a single word: Exam or Project
• You may choose one but not both!
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18. If you choose Exam
• It will be given during exam week
• Friday May 10th at 1230pm
• You will have 2 hours but shouldn’t need it.
• Test will be comprehensive.
• Strings
• For/while loops
• If statements
• Lists
• Dictionaries
• Very similar to the types of questions on the Midterm.
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19. If you choose Project
• Due Friday March 3rd by Midnight
• The project will be assigned on Friday April 5th
• You will receive a Project Specification which will need to be followed
thoroughly.
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