In this section you learned how to summarize quantitative data with a measure of spread.
In this section you learned how to summarize quantitative data with a measure of spread.
What 3 measures of spread were discussed in this section of the book?
1. __________________ 2. __________________ 3. __________________
NOTE: We will get a fourth measure called the IQR in the next section.
What is the symbol for population standard deviation?
population std dev = _____
What is the symbol for sample standard deviation?
sample std dev = ______
Chebyshev’s Theorem
For any set of data:
At least 75% of the data fall in the interval from __________ to __________.
At least 88.9% of the data fall in the interval from __________ to __________.
At least 93.8% of the data fall in the interval from __________ to __________.
Fill in the following as you work through your given problems in MyOpenMath
1. Fill in the following in the context of this problem:
Individual: _______________________________________________
Variable: ______________________________________(measured in mg/dL)
Type of variable: _______________________________________
Use StatCrunch to find the summary statistics for the given data.
Use can copy and paste the list of data from MyOpenMath into a column in StatCrunch.
Mean = _______ = __________ ______________ (symbol, value, units)
Median = __________ ______________ (value, units)
Range = __________________________ = ______________ __________ (compute, value, units)
Variance = _______ = __________ ______________ (symbol, value, units)
Standard Deviation = _______ = __________ ______________ (symbol, value, units)
2. Fill in the following in the context of this problem:
Individual: _______________________________________________
Variable: ______________________________________________
Type of variable: _______________________________________
Use StatCrunch to find the summary statistics for the given data.
Mean = _______ = __________ ______________ (symbol, value, units)
Median = __________ ______________ (value, units)
Range = __________________________ = ______________ __________ (compute, value, units)
Variance = _______ = __________ ______________ (symbol, value, units)
Standard Deviation = _______ = __________ ______________ (symbol, value, units)
Use StatCrunch to find the summary statistics for the data without the CEO salary.
Mean = _______ = __________ ______________ (symbol, value, units)
Median = __________ ______________ (value, units)
Range = __________________________ = ______________ __________ (compute, value, units)
Variance = _______ = __________ ______________ (symbol, value, units)
Standard Deviation = _______ = __________ ______________ (symbol, value, units)
Which of the above statistics was least affected by removing the CEO salary? __________________
• We will get another measure of variation called the IQR in the next section after we discuss measures of position (or rank). We will see that the IQR will not be affected by the CEO salary.
3. Fill in the following in the context of this problem:
Individual: _______________________________________________
Variable: ______________________________________(measured in mg/dL)
Type of variable: _______________________________________
Use StatCrunch to find the summary statistics for the given data.
Mean = _______ = __________ ______________ (symbol, value, units)
Median = __________ ______________ (value, units)
Range = __________________________ = ______________ __________ (compute, value, units)
Variance = _______ = __________ ______________ (symbol, value, units)
Standard Deviation = _______ = __________ ______________ (symbol, value, units)
4. Explain why this is a matched-pairs study:
Compare the means using common language and context from the problem
Compare the standard deviations using common language and context from the problem
5. Fill in the following in the context of this problem:
Individual: _______________________________________________
Variable: ______________________________________
Type of variable: _______________________________________
a. Use StatCrunch to find the mean and standard deviation of the data.
Mean = _______ = __________ ______________ (symbol, value, units)
Standard Deviation = _______ = __________ ______________ (symbol, value, units)
b. How far do you need to go from the mean to get at least 75% of a data set? _____________________
Compute the interval asked for: ( , )
Interpret in context: At least 75% of ….
c. How far do you need to go from the mean to get at least 88.9% of a data set? _____________________
Compute the interval asked for: ( , )
Interpret in context: At least 88.9% of ….
Compute the actual percentage of data in this interval: ___ ___ . ___%
Why does that answer have to be “yes”?
Is your computed percentage at least 88.9%? _________ ” ≈
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