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Descriptive Statistics and Probability Assignment
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Assignment Task
Descriptive Statistics and Probability
1. Look at the data given below. Plot the data, find the outliers and find out
|
Name of company |
Measure X |
|
Allied Signal |
24.23% |
|
Bankers Trust |
25.53% |
|
General Mills |
25.41% |
|
ITT Industries |
24.14% |
|
J.P.Morgan & Co. |
29.62% |
|
Lehman Brothers |
28.25% |
|
Marriott |
25.81% |
|
MCI |
24.39% |
|
Merrill Lynch |
40.26% |
|
Microsoft |
32.95% |
|
Morgan Stanley |
91.36% |
|
Sun Microsystems |
25.99% |
|
Travelers |
39.42% |
|
US Airways |
26.71% |
|
Warner-Lambert |
35.00% |
2.
Answer the following three questions based on the box-plot above.
- What is inter-quartile range of this dataset? (please approximate the numbers) In one line, explain what this value implies.
- What can we say about the skewness of this dataset?
- If it was found that the data point with the value 25 is actually 2.5, how would the new box-plot be affected?
3.
Answer the following three questions based on the histogram above.
- Where would the mode of this dataset lie?
- Comment on the skewness of the dataset.
- Suppose that the above histogram and the box-plot in question 2 are plotted for the same dataset. Explain how these graphs complement each other in providing information about any dataset.
4. AT&T was running commercials in 1990 aimed at luring back customers who had switched to one of the other long-distance phone service providers. One such commercial shows a businessman trying to reach Phoenix and mistakenly getting Fiji, where a half-naked native on a beach responds incomprehensibly in Polynesian. When asked about this advertisement, AT&T admitted that the portrayed incident did not actually take place but added that this was an enactment of something that “could happen.” Suppose that one in 200 long-distance telephone calls is misdirected. What is the probability that at least one in five attempted telephone calls reaches the wrong number? (Assume independence of attempts.)
5. Returns on a certain business venture, to the nearest $1,000, are known to follow the following probability distribution
|
x |
P(x) |
|
-2,000 |
0.1 |
|
-1,000 |
0.1 |
|
0 |
0.2 |
|
1000 |
0.2 |
|
2000 |
0.3 |
|
3000 |
0.1 |
1. What is the most likely monetary outcome of the business venture?
2. Is the venture likely to be successful? Explain
3. What is the long-term average earning of business ventures of this kind? Explain
4. What is the good measure of the risk involved in a venture of this kind? Compute this measure
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