Math 105 Topics

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Math 105 Topics

• Computing the standard deviation

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The Mean

• We know how to compute the mean. We just sum up
  all the values and divide by n
• The sum of values has a special notation. We use
  the ? (sigma) notation.
• n always refers to the number of data values

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An example

• Here is some data. We give it the name X.
• If we add (sum) these up we get 138
• Thus

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Example

• In this example n 7 (7 data values)
• Thus

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The standard deviation

• The sample standard deviation, s, is the square
  root of the sample variance, s2.

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Example
1. Subtract the mean from the values
2. Square each value
Setting up a table and follwing these 3 steps
will always work!
3. Sum the numbers
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Example continued
We then divide by n-1 to get the sample variance
The sample standard deviation is 7.02
Taking the square root gives us the standard
deviation
We divide by 6 since n7 in this example
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A quick Check

• Using StatCrunch

same results!
Column Statistics Summary statistics
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A better way

• There is an equivalent, but easier, way to
  compute the sample variance (and thus the sample
  standard deviation).

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Why is this easier?

• The computation introduces lots of
  decimal numbers into the computation.
• The new method has you compute ? x and ? x2 and
  the rest is just filling in the formula.

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Our example again
Square each value of X Form two sums, one of the
original data, the other of the squares of the
data
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Our example again
Now we fill in the formula
This agrees with our earlier computation.
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Our conclusion
It is tedious but not difficult.