ST 3001 Walden University Body Mass Index Worksheet

Assessment ST3001Instructions
Before submitting your Assessment, carefully review the rubric. This is the same
rubric the assessor will use to evaluate your submission and it provides detailed
criteria describing how to achieve or master the Competency. Many students find
that understanding the requirements of the Assessment and the rubric criteria help
them direct their focus and use their time most productively.
Rubric
Explaining Statistics to Your Boss
You are tasked with explaining some statistical concepts to your boss to help him
make some company decisions. Your boss does not have any background in statistics
and has a hard time with numbers in general, so you decide to choose a non-work
topic to explain the concepts. You will use Statdisk to make your computations, and
then present the information along with your explanations as a report. Your report
should include a title page, table of contents, summary of the information, your
computations and explanations, any conclusions that you make about the data, and
references that you used. Keep in mind that your textbook and the course resources
you use when making your computations and explanations should be cited
appropriately.
To prepare for this Assessment:
Download the Statdisk program from www.Statdisk.org. You will save this to your
computer for use throughout the Area of Expertise.
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For this Assessment, you will need to read pages 3–4 and 7–9 of the Statdisk
User Manual document.
Choose one of the following files from the Statdisk User Manual document:
o Oscar Winner (This file contains the age of each actress and actor Oscar
winner at the time of their win.)
o Freshman 15 (This file contains the weight in kilograms and BMI of
freshmen in September and in April.)
o Word Count (This file contains the counts of words spoken in a day by
male and female students in size different sample groups.)
Garbage Weights (This file contains the weights in pounds of household
garbage.)
o Passive and Active Smoke (This file contains the measured levels of
serum continine in ng/ml).
Note: You will need to choose two (2) quantitative variables from the file that
you chose and label them Variable 1 and Variable 2.
o
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Part 1: Computations and Graphical Representations
Part 2: Interpreting Statistical Information
Note: Use the learning resources throughout this competency to support your
computations and cite at least one resource.
Part 1: computations and graphical representations:
Make the following computations in Statdisk, and then copy your work into your
report.
Note: Be sure to copy all work into your report and to label your computations. In
your report, you should:
1. Determine the type of data (quantitative or qualitative) and the level of
measurement (nominal, ordinal, interval, ratio) for the data set. Explain how
you determined the type of data.
2. Find the mean, median, and midrange for the data in Variable 1. Paste your
results from Statdisk in your report.
3. Find the range, variance, and standard deviation for Variable 1. Paste your
results from Statdisk in your report.
o List any values for the first column that you think may be outliers. Why
do you think that? (Hint: You may want to look at the modified boxplot,
sort the data, and look at the smallest and largest values.)
4. Find the mean, median, and midrange for the data in Variable 2. Paste your
results from Statdisk in your file.
5. Find the range, variance, and standard deviation for Variable 2. Paste your
results from Statdisk in your file.
o List any values for the second column that you think may be outliers.
Why do you think that? (Hint: You may want to look at the modified
boxplot, sort the data, and look at the smallest and largest values.)
6. Find the five-number summary for the data in Variables 1 and 2. You will need
to label each of the columns with an appropriate measure in the top row for
clarity.
7. Compare the two variables from the dataset using a boxplot of Variables 1 and
2. Paste your boxplot in your file.
8. Create a histogram for Variables 1 and 2 data. Paste it in your file.
Part 2: Interpreting Statistical Information
Using the descriptive statistics calculated earlier, what conclusions can you make
when you compare the two variables? You will want to address each of the following
points below. Please be sure to use specific values to support your reasoning. You
must justify your conclusions with Statdisk results from the descriptive statistics,
histogram, and boxplot for each portion below.
Reminder: Your boss does not have any experience with statistics, so explain your
reasoning in a way that is understandable by all people. To justify your conclusions,
you should:
9. Explain one conclusion about a measure of center (mean, median, midrange).
10. Explain one conclusion about the variability in the two datasets (variance,
standard deviation, range).
11. Explain one conclusion about the shape of the distribution (by mentioning
direction of skew and the relationship of the mean and median).
Smoke Exposure Percentiles
Answer the following questions concerning the data in Table 4.3.
a. What is the percentile for the data value of 104.54 ng/ml for smokers?
b. What is the percentile for the data value of 61.33 ng/ml for nonsmokers?
c. What data value marks the 36th percentile for the smokers? For the nonsmokers?
SOLUTION The following results are approximate.
a. The data value of 104.54 ng/ml for smokers is the 35th data value in the set, which means
that 34 data values lie below it. Thus, its percentile is
number of values less than 104.54 ng/ml
total number of values in data set
*100=
34
50
*100=68
In other words, the 35th data value marks the 68th percentile.
b. The data value of 61.33 ng/ml for nonsmokers is the 50th and highest data value in the set,
which means that 49 data values lie below it. Thus, its percentile is
number of values less than 61.33 ng/ml
total number of values in data set
*100=
49
50
*100=98
In other words, the highest data value in this set lies in the 98th percentile.
c. Because there are 50 data values in the set, the 36th percentile is around the 0.36*50 =
18th value. For smokers, this value is 20.16 ng/ml; for nonsmokers, it is 0.33 ng/ml.
Standard Deviation
The five-number summary characterizes variation well, but there are advantages to describing
variation with a single number. The single number most commonly used to describe variation
is called the standard deviation.
The standard deviation is a measure of how widely data values are spread around the mean
of a data set. To calculate a standard deviation, we first find the mean and then find how
much
each data value “deviates” from the mean. Consider the data sets of waiting times at banks, for
which the mean waiting time was 7.2 minutes for both Big Bank and Best Bank. For a waiting
time of 8.2 minutes, the deviation from the mean is equal to 8.2 minutes -7.2 minutes =1.0
minute, meaning that it is 1.0 minute greater than the mean. For a waiting time of 5.2 minutes,
the deviation from the mean is equal to 5.2 minutes -7.2 minutes =-2 minutes (negative
2 minutes), because it is 2.0 minutes less than the mean.
In essence, the standard deviation is a measure of the average of all the deviations from
the mean. However, if we simply computed the mean of all the deviations, the result would
always be zero, because the positive deviations exactly balance the negative deviations.
Therefore, we instead use the procedure in the following box, in which we make all the values
positive by first squaring all the deviations (because squares are always positive or zero)
calculating the Standard Deviation
To calculate the standard deviation for any data set:
Step 1. Compute the mean of the data set. Then find the deviation from the mean for every
data value by subtracting the mean from the data value. That is, for every data value,
deviation from mean=data value-mean
Step 2. Find the squares of all the deviations from the mean.
Step 3. Add all the squares of the deviations from the mean.
Step 4. Divide this sum by the total number of data values minus 1.
Step 5. The standard deviation is the square root of this quotient. Overall, these steps can be
summarized in the following standard deviation formula:
standard deviation=C
sum of (deviations from the mean)
2
total number of data values-1
Note that, because we square the deviations in Step 3 and then take the square root in Step 5,
the units of the standard deviation are the same as the units of the data values. For example,
if the
data values have units of minutes, the standard deviation also has units of minutes. (The result
of Step 4 is called the variance of the distribution. It is the square of the standard deviation and
therefore has units that are squares of the units used for the original data; for example, if the original
data are in meters, the variance will be in units of meters
2. Although the variance is used in many
advanced statistical computations, we