Harper MTH165 Homework Section 3.2 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 3.2

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%? _________ "         ≈