91Ó°ÊÓ

A survey of enrollment at $35$community colleges across the United States yielded the following figures:

$$\begin{gathered} 6414;1550;2109;9350;21828;4300;5944;5722;2825; \\ 2044;5481;5200;5853;2750;10012;6357;27000;9414; \\ 7681;\text{3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493;} \\ \text{2771; 2861; 1263; 7285; 28165; 5080;}11622 \end{gathered}$$

a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."

b. Construct a histogram of the data.

c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?

d. Calculate the sample mean.

e. Calculate the sample standard deviation.

f. A school with an enrollment of $8000$would be how many standard deviations away from the mean?

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table.

Use the following information to answer the next two exercises. X= the number of days per week that $100$clients use a particular exercise facility.

The number that is $1.5$standard deviations BELOW the mean is approximately

$$\begin{gathered} a.0.7 \\ b.4.8 \\ c.-2.8 \\ d.Cannotbedetermined \end{gathered}$$

Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the$Table2.83.$

a. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.

b. If a data value is identified as an outlier, what should be done about it?

c. Are any data values further than two standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)

d. Do parts a and c of this problem give the same answer?

e. Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?

f. Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?

What does the relative frequency column in Table $2.42$ sum to? Why?

$2.42$What is the difference between relative frequency and frequency for each data value in Table $2$?

What is the difference between cumulative relative frequency and relative frequency for each data value?

To construct the histogram for the data in Table $2.42$, determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram. Label the horizontal and vertical axes with words. Include numerical scaling.

Construct a frequency polygon for the following:

a.

b.

c.

Construct a frequency polygon from the frequency distribution for the $50$ highest ranked countries for depth of hunger