*Mathematics and Statistics I*

*HW1 Oct 2 ^{nd} *

Discuss advantages and disadvantages of qualitative/quantitative methods based on the following two articles:

HYPERLINK "http://web.mnstate.edu/robertsb/390/TOURISM%20AND%20SEASONAL%20RETIREMENT%20MIGRATION.pdf" http://web.mnstate.edu/robertsb/390/TOURISM%20AND%20SEASONAL%20RETIREMENT%20MIGRATION.pdf

HYPERLINK "https://www.bebr.ufl.edu/sites/default/files/J%20Geront%202006%20%28Elder%20Migr%29.pdf" https://www.bebr.ufl.edu/sites/default/files/J%20Geront%202006%20%28Elder%20Migr%29.pdf

With the help of some TV guide (printed or on the web), try to produce a number comparing the representation of men and woman on TV. For that purpose, count the numbers of women and men mentioned/depictured within a week on one channel, or on one day on several channels. Or, as an alternative, watch or listen the daily news for one week and stop how much time is dedicated to individual male/female persons.

Give a striking statistical figure (“number”, e.g. from the newspaper, the internet, an article or a book) which you consider – for what reason ever – memorable, and explain why you think so. Are there weaknesses or potential weaknesses regarding this figure?

Mathematics and Statistics I

HW2 Oct 9^{th}

- Visit the Webpage at Statistics Austria http://www.statistik.at/web_en/statistics/tourism/accommodation/arrivals_overnight_stays/index.html and have a look at the tables there. Are they informative? Is it easy to get out a message? Do you like them? Would you, for a presentation of your own, change anything?
- Suppose a newspaper would report that 80% of Austrians suffering a heart attack have regularly eaten Schnitzel (a popular meat dish) before. What can we conclude?

- You shall report about victims of the civil war in Syria. Would you rather choose absolute or relative frequencies?

- Rate all European countries according to the following categories (no matter whether you have been already there or not): 1 no urge to go there at all, 2 happy to go there if I have to, 3 hope to go there one time, 4 will actively try to go there in the near future. Construct a frequency table with absolute and relative frequencies, percentages and cumulative percentages.

- Revising the number of complaints about your employees, you obtain the following data for 20 people:

1, 0, 0, 4, 18, 3, 6, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2

Draw a frequency table with absolute and relative frequencies, percentages and cumulative percentages.

Draw the same frequency frequency table under the assumption that there have been another 5 cases for whom no data are available.

6.Bonus: The following text (taken from http://courses.ncssm.edu/math/Stat_Inst/PDFS/REG3_LOG.pdf) gives (famous) data about the observed damages of O-rings in the US space shuttle Challenger, available when it was decided that the Challenger should start on a cold winter day with 31° Fahrenheit temperature. The shuttle exploded and all 7 passengers died. Could it have been predicted that the O-rings would not hold? What are your thoughts?

(For the interested: see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.15.1047&rep=rep1&type=pdf

regarding the flaws in the decision making process.)

*Mathematics and Statistics I*

*HW3 Oct 16 ^{th} *

Reading assignment preparing *next lecture*:

Read pp. 27-34 and pp. 44-53 in the Jaisingh book (Statistics for the Utterly Confused).

For the exercises:

You investigate how waiters and waitresses in a certain (fictitious) region assess their satisfaction with work-life-balance regarding their job. The following scores are observed (large scores indicate problems with work-life-balance):

Men: 33, 13, 16, 10, 19, 23, 12, 11, 13, 12

Women: 18, 13, 23, 26, 10, 25, 19, 18

Compute mean and median for both subsamples and for the total sample.

3Demonstrate how the grand mean can be computed using the gender averages (weighted mean formula). Does the same work with the median as well? (Just try out!)

4 From experience, you expect 50% of the women to prefer menu A to menu B, but only 35% of the men. Your guest list for lunch shows 75% men and only 25% women. How many people will prefer menu A?

5 Assessing the satisfaction with the management of a hotel, you receive the following results from 5 employees [scale 1-10, 1= not satisfied, 10=highly satisfied]:

3, 8, 6, 7, 10, 8

Compute mean, median and mode.

Interpret your results. What do these measures tell you about the satisfaction of the employees?

6 Read the Wikipedia article about the heights of US presidents’ heights.

HYPERLINK "http://en.wikipedia.org/wiki/Heights_of_presidents_and_presidential_candidates_of_the_United_States" http://en.wikipedia.org/wiki/Heights_of_presidents_and_presidential_candidates_of_the_United_States

Compare mean, mode and median of the latest 10 presidents to those of the latest ten not inaugurated candidates. What about the heights of the candidates in general?

*Mathematics and Statistics I*

*Homework 5*

*Oct 29 ^{th} *

The following numbers reflect the prices which several hotels located in the same skiing resort charge for a twin room for one night:

270, 160, 170, 130, 170, 1400, 270, 160, 270, 270

Compute MAD, variance and standard deviation. What would be the results replacing that outlier “1400” by “400”?

For a certain type of wellness package, a hotel manager wants to specify the typical consumer. Therefore, he/she talks to the clients and tries to find out about their profession, which he/she turns into a measure of socio-economic status according to standard tables. Suppose the following numbers would be the result, what would they tell you? Use a) mean and standard deviation for the comparison, and b) median and interquartile range.

Consumers: 20, 89, 32, 22, 90, 78, 60, 67

Non-consumers: 42, 58, 64, 30, 20, 53, 75, 54

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