# Math 221 Lab Week 2 Name: Statistical Concepts:

**Math 221 − Lab Week 2**

Name:

Statistical Concepts:

• Using Statcrunch

• Graphics

• Shapes of Distributions

• Descriptive Statistics

• Empirical Rule

Follow the directions for each problem and then answer the questions that follow in the space provided.

**Background Info:** The American International Group (AIG) was once the 18th largest corporation in the world. In 2004, AIG stock hit an all-time high of $76.77, putting its market value at nearly $300 billion. By early 2007 AIG had assets of $1 trillion, $110 billion in revenues, 74 million customers and 116,000 employees in 130 countries and jurisdictions. Yet just 18 months later, AIG found itself on the brink of failure and in need of emergency government assistance. AIG was one of the largest beneficiaries of the U.S. government’s Troubled Asset Relief Program (TARP), established in 2008 during the financial crisis to purchase assets and equity from financial institutions. Between 2007 and 2009 AIG stock lost more than 99% of its value, hitting $0.35 in early March. (Source: Business Statistics, 3rd edition, Norean D. Sharpe)

Dataset “**AIG Stock Prices**” gives the monthly average stock price (in dollars) from 2002-2007, which was the six years leading up to the company’s crisis. This dataset can be found under Files, Week 2, Datasets.

**1. Create a histogram for the monthly average stock prices **

• Open up the Statcrunch program.

• Copy the **non-rounded** stock price data from Excel and paste it into Statcrunch (use CTRL + V to paste).

• Click on Graph, then Choose Histogram.

• Click on the variable name under Select Column(s).

• Under Bins, enter 45 for Start At and 5 for Width

• Under Display Options, check Value Above Bar

• Under Markers, check Mean

• Under Graph Properties, label the x-axis “Average Stock Price (in dollars)”, the y-axis “# of Months (2002-2007)”, and the chart title “AIG Monthly Stock Prices from 2002-2007”.

• Click on Compute.

• Right click on image and choose Copy Image

• Paste in the gray field below by pressing (CTRL + ALT + V) then choose Device Independent Bitmap.

a. Describe the shape of the distribution of the monthly average stock prices. (i.e. Is it symmetric, uniform,

skewed, etc? If skewed, what type of skewness?)

b. Using the histogram, how many months between 2002 and 2007 had a monthly average stock price less

than $65?

c. The green vertical line represents the mean of the monthly average stock prices. Give a best estimate for

it from the graph.

a.

b.

c.

**2. Stem-and-Leaf Plot for Rounded Monthly Average Stock Prices **

Using the same AIG dataset, construct a stem-and-leaf plot for the Monthly Average Stock Prices. For your convenience, stock prices have been rounded to the nearest whole number.

**Steps to Create a Stem and Leaf Plot in Statcrunch:**

• Open up Statcrunch

• Copy and Paste the **rounded** stock prices into Statcrunch

• Click on Graph, then Choose Stem and Leaf.

• Click on the variable title for the rounded stock prices.

• Hit Compute

• To copy, highlight the stem-and -leaf plot and paste it into the answer field below.

a. Compare the shape of the distributions from the stem-and-leaf plot and the histogram above. What can you

conclude? Is this surprising to you? Explain.

b. If you had to find the median monthly average stock price from the stem-and-leaf plot, explain how you would

go about doing so. What is the median monthly average stock price?

c. From the graph, find the mean for the 6 largest monthly average stock price.

a.

b.

c.

**3. Boxplot for Monthly Average Stock Prices**

Using the AIG dataset, construct a boxplot for the variable monthly average stock prices. Follow the steps below:

• Open up Statcrunch

• Use the **non-rounded** monthly average stock prices.

• Click on Graph, then choose Boxplot.

• Click on the appropriate variable.

• Under Other Options, check “Draw Boxes Horizontally”.

• Under Graph Properties, as in part 1, enter an appropriate x-axis label (include units) and a title.

• Hit Compute

• Copy and paste below following the same instructions as on the Histogram.

a. Give the 5-number summary. (Hint: Hover cursor over boxplot)

b. What percent of all monthly average stock prices fall within Q1 and the max value?

c. What does the line within the box represent and what is its value?

d. If you had to find the range for the dataset using the box plot values, how would you find it? What is the

range?

a.

Min =

Q1 =

Q2 =

Q3 =

Max =

b.

c.

d.

**4. Calculating Descriptive Statistics for Monthly Average Stock Prices**

Using the AIG dataset, use the tools you learned in week 1 to find the descriptive statistics for the **non-rounded **monthly average stock prices. Fill in the table below. **Round answers to two decimal place, when appropriate**.

Mean

Median

Range

Variance

Standard Deviation

Price

a. What statistics above are values that describe the central tendency of the data?

b. What statistics above are values that describe the variation of the data?

c. All statistic above have the same units, except for one of them. Which statistic has different units and what are its units?

a.

b.

c.

**5. Empirical Rule for Monthly Average Stock Prices**

Although the Monthly Average Stock Prices have a slight skewness, it can be argued that it does follow an approximately bell-shaped distribution. Use what you learned in week 1 about the Empirical Rule to answer the questions that follow. It will be helpful to draw the distribution on a scratch paper and label it using the mean and standard deviation that you found in part 4 above. See your week one lecture notes.

a. 95% of the monthly average stock prices between 2002 and 2007 fell between what two values? **Either show the math calculations or explain in words how your answers were calculated.**

a.

b. 68% of the monthly average stock prices between 2002 and 2007 fell between what two values? **Either show the math calculations or explain in words how your answers were calculated.**

b.

**Upon completing this lab, save it by including your name at the end of the file name. Under Modules, Week 2: Lab, upload your saved document and submit it by the due date of Sunday, 1/14 by 11:59pm. **