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HW #93 Answers:
1. 6.2 hrs
2. -.2, -2.2, -.2, .8, 1.8
3. 1, 4, 6, 8, 12 or 11, 10, 1, 1, 8, etc...
4.
5. 11.7 hours
6.
7. a. Greater, data is more spread out
c. 610 hours
b. 36 students
8. a. 11 students
d. 16.94 hrs
Mixed Review: 20 terms
Aim #94: How do we calculate the standard deviation of a data set?
Do Now:
move dot!
What is the mean of this data set?
What is the typical deviation from the mean?
Standard Deviation
Standard deviation is a measure of variability in a data set.
The steps to calculate the standard deviation are:
1. Determine each deviation from the mean.
2. Square the deviations from the mean.
3. Sum up all the squared deviations.
The number of values in a data set is denoted by n.
4. Next we divide the sum of the squares by n - 1.
This is called the variance.
5. Finally we take the square root of that value to obtain the
standard deviation.
The unit of the standard deviation is always the same as the unit of the
original data set.
The larger the standard deviation, the greater the spread (variability)
of the data set.
Now you can calculate the standard deviation of the lifetimes for the
eight Brand B batteries. The mean was 100.5. We already have the
deviations from the mean:
Jenna has bought a new hybrid car. Each week for a period seven
weeks she has noted the fuel efficiency (in miles per gallon) of her
car. The results are shown below.
45
44
43
44
45
44
43
Ten people attended a talk at a conference. At the end of the talk, the attendees
were given a questionnaire that consisted of four questions. The questions were
optional, so it was possible that some attendees might answer none of the
questions while others might answer 1, 2, 3, or all 4 of the questions (so the possible
numbers of questions answered are 0, 1, 2, 3, and 4). Suppose that the numbers of
questions answered by each of the ten people were as shown in the dot plot below.
What is the standard deviation?
To find the mean and standard deviation using the calculator, follow
the steps below.
1. From the home screen, go to STAT, then EDIT.
2. Type the data into L1.
3. Press 2ND, QUIT to return to the home screen.
4. Press STAT, select CALC, select 1-Var Stats, press ENTER.
5. The screen should now show summary statistics for your data set. The
mean is the x value, and the standard deviation is the sx value.
Suppose the dot plot looked like this:
a) Use your calculator to find the mean and the standard deviation
of this distribution.
b) Remember that the size of the standard deviation is related to
the size of the deviations from the mean. Explain why the standard
deviation of this distribution is greater than the standard deviation
in the Do Now.
Suppose that every person answers all four questions on the
questionnaire.
a) What would the dot plot look like?
b) What is the mean number of questions answered? (You should
be able to answer without doing any calculations!)
c) What is the standard deviation? (Again, don‛t do any
calculations!)
A set of eight men had heights (in inches) as shown below.
67.0
70.9
67.6
69.8
69.7
70.9
68.7
67.2
Find the mean and standard deviation using your calculator to the
nearest hundredth.
Mean: _________
Standard Deviation: ___________
Sum It Up!
The standard deviation measures a typical deviation from the mean.
To calculate the standard deviation,
1. Find the mean of the data set
2. Calculate the deviations from the mean
3. Square the deviations from the mean
4. Add up the squared deviations
5. Divide by n – 1 (if you are working with a data from a sample,
which is the most common case)
6. Take the square root
The unit of the standard deviation is always the same as the unit of
the original data set.
The larger the standard deviation, the greater the spread (variability)
of the data set.
The mean and the standard deviation of a data set can be found directly
using the statistical features of a calculator.
The size of the standard deviation is related to the sizes of the
deviations from the mean. Therefore, the standard deviation is
minimized when all the numbers in the data set are the same and is
maximized when the deviations from the mean are made as large as
possible.