Assessment ST3001Instructions

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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.

•

•

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

•

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

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