Download Notes: 5.3 Standard Deviation

5.3 – Standard Deviation
Foundations of Math 11
Key Terms:
Deviation: the difference between a data value and the ______________ for the same set of data
Standard Deviation: a measure of the ________________ or scatter of the data in relation to the mean
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essentially the standard deviation measures the spread of the data
a low standard deviation means the data is close to the mean (concentrated)
a high standard deviation means the data is far from the mean (spread out)
Example: Which of the following histograms has a greater standard deviation?
Symbols:
X = mean
S = sum
s = SD N = # of values
Calculating the Standard Deviation:
1. Calculate the mean
2. Find the difference of each value and the mean
3. Sum all the differences
4. Divide the sum by the # of values minus 1 (n)
5. Take the square root
∑(𝑥−𝑥̅ )2
𝑁−1
∑(𝑥−𝑥̅ )2
√
𝑁−1
Example:
The rest of this example will be done in the case where we have a sample size of 5 pirates; therefore we will
be using the standard deviation equation for a sample of a population.
Here are the amounts of gold coins the 5 pirates have: 4, 2, 5, 8, 6
Now, let's calculate the standard deviation:
Homework:
Do: P. 233 1, 2, 3, 5, 7, 10 13, + Standard Deviation Worksheet
5.3 – Standard Deviation
Foundations of Math 11
1. Calculate the mean:
2. Calculate
for each value in the sample:
3. Calculate
:
4. Calculate the standard deviation:
The standard deviation for the amounts of gold coins the pirates have is 2.24 gold coins.
Example 2:
Calculate the mean and standard deviation for the following data, which are marks from a class:
(Follow Steps 1-4, show work on a separate piece of paper)
Name
Mark
Name
Mark
Bill
78.2
Joe
91.5
Will
Jill
76.9
84.3
Mo
Floe
96.4
85.8
Trill
88.6
Row
80.2
Homework:
Do: P. 233 1, 2, 3, 5, 7, 10 13, + Standard Deviation Worksheet