# Chapter 3: Descriptive Measures

3.171

Hurricanes. An article by D. Schaefer et al. (journal of Tropical Ecology, Vol. 16, pp. 189-207) reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experimental Forest in Puerto Rico. The study shows that Hurricane Hugo had a significant impact on stream water chemistry. The following table shows a sample of 10 ammonia fluxes in the first year after Hugo. Data are in kilograms per hectare per year.

a. obtain and interpret the quartiles.

b. determine and interpret the interquartile range.

c. find and interpret the five-number summary:

d. identify potential outliers, if am:

e. construct and interpret a boxplot.

Boxplots

Q.3.179 Hospital stays.the U.S National center for health statistics compiles data on the length of stay by patients in short-term hospitals and publishes its finding in vital and Heath statistics. A random sample of 21 patients yielded the following data on the length of stay, in days.

a. obtain and interpret the quartiles.

b. determine and interpret the interquartile range.

c. find and interpret the five number summary.

d. identify potential outliers, if any

e. construct and interpret a boxplot.

Q. 1

Define

a. descriptive measures,

b. measures of center,

c. measures of variation.

Q. 10

A data set with roughly a bell-shaped distribution has mean $45$and standard deviation $12.$Approximately what percentage of the observations lie between $33$and $57$?

Q. 11

A data set of size $152$with roughly a bell-shaped distribution has mean $25$and standard deviation$4$$4$.

Approximately how many observations lie between$17$ and $33$ ?

Q. 12

Regarding the five-number summary:

a. Identify its components.

b. How can it be employed to describe center and variation?

c. What graphical display is based on it?

Q. 13

Regarding outliers:

a. What is an outlier?

b. Explain how you can identify potential outliers, using only the first and third quartiles.

Q. 14

Regarding$z$-scores:

a. How is a $z$-score obtained?

b. What is the interpretation of a $z$-score?

c. An observation has a $z$-score of $2.9$. Roughly speaking, what is the relative standing of the observation?

Q. 15

An integral part of doing business in the dot-com culture of the late $1990$swas frequenting the party circuit centered in San Francisco. Here high-tech companies threw as many as five parties a night to recruit or retain talented workers in a highly competitive job market. With as many as$700$guests at a single party. the food and booze flowed, with an average alcohol cost per guest of dollarrole="math" localid="1651238902534" $15$to$18$ and an average food bill of dollar $75$to$150$. A sample of guests at a dot-com party yielded the following data on number of alcoholic drinks consumed per person.

a. Find the mean, median, and mode of these data.

b. Which measure of center do you think is best here? Explain your answer.

Q. 16

Duration of Marriages. The National Center for Health Statistics publishes information on the duration of marriages in Vital Statistics of the United States. Which measure of center is more appropriate for data on the duration of marriages, the mean or the median? Explain your answer.