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

a. Exam scores (9 students) 42, 55, 65, 67, 68, 75, 76, 78, 94

b. GPAs (8 students) 2.25, 2.55, 2.95, 3.02, 3.04, 3.37, 3.51, 3.66

c. Class absences (12 students) 0, 0, 0, 0, 0, 1, 2, 3, 3, 5, 5, 15

Complete the statement with the correct function from the table below.

______ grows at a constant percent rate per unit interval.

$$\begin{array}{|c|c|c|} \hline \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{g}(\boldsymbol{x}) \\ \hline 0 & 50 & 100 \\ \hline 1 & 54 & 104 \\ \hline 2 & 58 & 108 \\ \hline 3 & 63 & 112 \\ \hline 4 & 68 & 116 \\ \hline 5 & 73 & 120 \\ \hline \end{array}$$

The test scores on a 100-point test were recorded for 20 students: 61 93 91 86 55 63 86 82 76 57 94 89 67 62 72 87 68 65 75 84 a. Use an appropriate graph to describe the data. b. Describe the shape and location of the scores. c. Is the shape of the distribution unusual? Can you think of any reason the distribution of the scores would have such a shape?

Use the following information. The table below shows the rebounding totals for the 2003 Los Angeles Sparks.

$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline 141 & 231 & 220 & 126 & 175 & 55 & 29 & 68 & 19 & 32 & 19 & 21 & 6 & 23 & 1 \\ \hline \end{array}$$

Which measure of central tendency best represents the data? Explain.

The numbers of various multiple births in the United States for the past 10 years are listed. Determine the range, variance, and standard deviation of the data sets. Which set of data is the most variable?

Triplets			Quadruplets			Quintuplets
5877	7110	5937	345	468	369	46	85	91
6898	6118	6885	434	355	501	69	67	85
6208	6742	6750	418	506	439	68	77	86
	6742			512			67

In the first-order decomposition of acetone at $500^{\circ} \mathrm{C}$

$$\mathrm{CH}_3 \mathrm{COCH}_3(g) \longrightarrow \text { products }$$

It is found that it takes $12.7 \mathrm{~h}$ to decompose $0.0622 \mathrm{M}$ acetone to $0.0133 M$. (a) Find $k$ at $500^{\circ} \mathrm{C}$. (b) What is the rate of decomposition when $\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]=0.0500 \mathrm{M}$ ? (c) How many minutes will it take to decompose enough acetone so that $68 \%$ remains?

Make a stem-and-leaf plot of the data. $$ \begin{matrix} \text{Test Scores (\\%)} & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ }\\ \text{87} & \text{82} & \text{95} & \text{91} & \text{69} & \text{ } & \text{ } & \text{ }\\ \text{88} & \text{68} & \text{87} & \text{65} & \text{81}\\ \text{97} & \text{85} & \text{80} & \text{90} & \text{62}\\ & \text{ }\\ \end{matrix} $$

For a recent year, the number of murders in 25 selected cities is shown. Construct a frequency distribution using 9 classes, and analyze the nature of the data in terms of shape, extreme values, etc.

$$\begin{array}{rrrrr}248 & 348 & 74 & 514 & 597 \\ 270 & 71 & 226 & 41 & 39 \\ 366 & 73 & 241 & 46 & 34 \\ 149 & 68 & 73 & 63 & 65 \\ 109 & 598 & 278 & 69 & 27\end{array}$$

a. Temperature measured in degrees Fahrenheit is a linear function of temperature measured in degrees Celsius. Use the fact that $0^{\circ}$ Celsius is equal to $32^{\circ}$ Fahrenheit and $100^{\circ}$ Celsius is equal to $212^{\circ}$ Fahrenheit to write an equation for this linear function. b. Use the function you obtained in part (a) to convert $15^{\circ}$ Celsius to Fahrenheit. c. Convert $68^{\circ}$ Fahrenheit to Celsius. d. What temperature is the same in both the Celsius and Fahrenheit scales?

Scientists have decided that there may be a relationship between temperature and the number of chirps produced by crickets. The table gives the temperature and the number of chirps per minute for several cricket samples.

Temperature ('F)	Chirps/min
71	138
68	97
75	152
80	158
60	81
75	155
84	165
Use the given data, suppose the outside temperature is $55^{\circ}$. About how many chirps per minute would you expect from a cricket?

The upper arm length of females over 20 years old in the United States is approximately Normal with mean 35.8 centimeters (cm) and standard deviation 2.1 cm. Use the 68-95-99.7 rule to answer the following questions. (Start by making a sketch like the given figure.)

(a) What range oflengt hs covers almost all (99.7%) of this distribution?

(b) What percent of women over 20 have upper arm lengths less than 33.7 cm?

The formula

$$S ( t ) = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } ^ { \prime }$$

can be used to determine the position S(t) of an object after t seconds at a rate of acceleration a with initial velocity

$$v_0$$

Valerie's car can accelerate 0.002 miles per second squared. How long will it take Valerie to match the average speed of highway traffic of 68 miles per hour? (Hint: Use acceleration * time = velocity.)

Leonardo da Vinci (1452-1519) drew a sketch of a man, indicating that a person's armspan (measuring across the back with your arms outstretched to make a "T") is roughly equal to the person's height. To test this claim. We measured eight people with the following results:

Person: 1, 2, 3, 4, 5, 6, 7, 8 Armspan (inches): 68, 62.25, 65, 69.5, 68, 69, 62, 60.25 Height (inches): 69, 62, 65, 70, 67, 67, 63, 62

a. Draw a scatterplot for armspan and height. Use the same scale on both the horizontal and vertical axes. Describe the relationship between the two variables. b. If da Vinci is correct, and a person's armspan is roughly the same as the person's height, what should the slope of the regression line be? c. Calculate the regression line for predicting height based on a person's armspan. Does the value of the slope b confirm your conclusions in part b? d. If a person has an armspan of 62 inches, what would you predict the person's height to be?

Substitute $t=0,10,20, \ldots, 70$ into the exponential function used in this section to model the US population 1790-1860. Compare the predicted values of the population with the actual values.

t	P	t	P	t	P	t	P
0	95	26	1108	54	1674	75	1739
5	222	33	1358	61	1710	81	1750
12	470	40	1527	68	1724	87	1755
19	800	47	1621