For each data set, find the median, midrange, and geometric mean. (b) Are they reasonable measures of central tendency? Explain.

Exam scores ($9$ students) $\quad 42,55,65,67,68,75,76,78,94$

The table below gives the life expectancy at birth for selected countries in North, Central, and South America for 1994.

Life Expectancy at Birth (years)

Make a box-and-whisker plot of the life expectancy for both genders.

From the union's platform, what conclusion can you draw about the status of labor in industrial America? What obstacles and challenges do Powderly and his fellow Knights identify as stumbling blocks to the equitable society they sought?

Reread the response you freewrote at the start of this discussion. Are your ideas on what it means to be an American closer to those of Hughes, Hine, or Lazarus? Pair up with a classmate and discuss how one or both of the poems or the photo challenges or supports your view. Try to find at least one point that might cause you to change or expand on your opinion. Do the same for your partner — that is, listen to his or her freewriting and suggest a connection to “The New Colossus,” the Hine photo, or “Let America Be America Again,” or something that might change or expand on the initial response.

Write the mathematical formula for a standardized variable.

In a sample of $10,000$ observations, about how many observations would you expect beyond $3$ standard deviations of the mean?

In a normal distribution, approximately what percent of observations are within $1$, $2$, and $3$ standard deviations of the mean?

An executive’s telephone log showed the lengths of 65 calls initiated during the last week of July.

(a) Sort the data.

(b) Find the mean, median, and mode.

(c) Do the measures of center agree? Explain.

(d) Are the data symmetric or skewed? If skewed, which direction?

$$\begin{array}{rrrrrrrrrr}1 & 2 & 10 & 5 & 3 & 3 & 2 & 20 & 1 & 1 \\ 6 & 3 & 13 & 2 & 2 & 1 & 26 & 3 & 1 & 3 \\ 1 & 2 & 1 & 7 & 1 & 2 & 3 & 1 & 2 & 12 \\ 1 & 4 & 2 & 2 & 29 & 1 & 1 & 1 & 8 & 5 \\ 1 & 4 & 2 & 1 & 1 & 1 & 1 & 6 & 1 & 2 \\ 3 & 3 & 6 & 1 & 3 & 1 & 1 & 5 & 1 & 18 \\ 2 & 13 & 13 & 1 & 6 & & & & & \end{array}$$

The management of a theme park obtained a random sample of the ages of $36$ riders of its Space Adventure Simulator. (a) Make a nice histogram. (b) Did your histogram follow Sturges' Rule? If not, why not? (c) Describe the distribution of sample data. (d) Make a dot plot of the data. (e) What can be learned from each display (dot plot and histogram)?

$$\begin{array}{rrrrrrrrr}39 & 46 & 15 & 38 & 39 & 47 & 50 & 61 & 17 \\ 40 & 54 & 36 & 16 & 18 & 34 & 42 & 10 & 16 \\ 16 & 13 & 38 & 14 & 16 & 56 & 17 & 18 & 53 \\ 24 & 17 & 12 & 21 & 8 & 18 & 13 & 13 & 10\end{array}$$

What is an outlier? An unusual data value?

To what kind of data does the Empirical Rule apply?

To what kind of data does Chebyshev's Theorem apply?

Which statement is false? Explain.

a. Sampling error can be reduced by using appropriate data coding.

b. Selection bias means that respondents are not typical of the target population.

c. Simple random sampling requires a list of the population.

On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner for 28 four-person tables.

(a) Find the mean, median, and mode.

(b) Do these measures of center agree? Explain.

(c) Make a histogram or dot plot.

(d) Are the data symmetric or skewed? If skewed, which direction?

$$\begin{array}{rrrrrrr}95 & 103 & 109 & 170 & 114 & 113 & 107 \\ 124 & 105 & 80 & 104 & 84 & 176 & 115 \\ 69 & 95 & 134 & 108 & 61 & 160 & 128 \\ 68 & 95 & 61 & 150 & 52 & 87 & 136\end{array}$$