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Exam 3: Statistics for Describing, Exploring, and Comparing Data

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Question 1

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A school has three tenth grade classes. All three classes took the same physics test. The mean scores for the three classes were 75, 71, and 78. Can the mean score for all tenth grade students be found by taking the mean of 75, 71, and 78? Explain.

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Unless the class sizes are equal, the me...

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Question 2

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Find the mean of the data summarized in the given frequency distribution. -The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $\begin{array} { r | r } \text { Speed (mph) } & \text { Cars } \\\hline 30 - 39 & 3 \\40 - 49 & 16 \\50 - 59 & 52 \\60 - 69 & 16 \\70 - 79 & 13\end{array}$

A) 59.3 mph
B) 56.5 mph
C) 62.2 mph
D) 54.5 mph

E) None of the above
F) A) and D)

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Question 3

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Find the mode(s) for the given sample data. -Listed below are the lengths (in inches) of each snake in the Clarmont Zoo's reptile house. $\begin{array} { l l l l l l l l l l l } 9 & 15 & 99 & 13 & 16 & 101 & 40 & 10 & 14 & 17 & 102\end{array}$

Elaine gets quiz grades of 60, 86, and 78. She gets a 70 on her final exam. Find the weighted mean if the quizzes each count for 20% and the final exam counts for 40% of the final grade. Round to one decimal place.

A city has 4 different area codes for phone numbers. Does it make sense to find the mean of these area codes?

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the standard deviation. Round your answer to one decimal place. $\begin{array} { c | r } \text { Height (in.) } & \text { Frequency } \\\hline 70 - 71 & 3 \\72 - 73 & 7 \\74 - 75 & 16 \\76 - 77 & 12 \\78 - 79 & 10 \\80 - 81 & 4 \\82 - 83 & 1\end{array}$

Find the median for the given sample data. -The temperatures (in degrees Fahrenheit) in 7 different cities on New Year's Day are listed below. $\begin{array} { l l l l l l l } 17 & 22 & 39 & 58 & 67 & 69 & 85\end{array}$ Find the median temperature.

Find the percentile for the data value. -In a data set with a range of 64.5 to 103 and 300 observations, there are 207 observations with values less than 88.5. Find the percentile for 88.5.

A student earned grades of 74, 75, 79, and 91 on her four regular tests. She earned a grade of 75 on the final exam and 84 on her class projects. Her combined homework grade was 86. The fou regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts for 10%, and homework counts for 20%. What is her weighted mean grade? Round to one decimal Place.

Find the variance for the given data. Round your answer to one more decimal place than the original data. -The weights (in ounces) of 10 cookies are shown. $\begin{array} { c c c l c } 1.12 & 0.92 & 1.44 & 1.28 & 0.97 \\ 1.03 & 1.14 & 0.85 & 1.4 & 0.95 \end{array}$ A) $0.042 \mathrm { oz } ^ { 2 }$ B) $0.038 \mathrm { oz } ^ { 2 }$ C) $0.034 \mathrm { oz } ^ { 2 }$ D) $0.032 \mathrm { oz } ^ { 2 }$

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. -The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in meters) are listed below. $\begin{array} { l l l l l l l } 0.453 & 0.401 & 0.596 & 0.388 & 0.649 & 0.279 & 0.551\end{array}$

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The number of assists per match for the setter on your school's volleyball team has a mean of 55 and a standard deviation of 8. How many standard deviations from the mean is an outing with 74 assists?

The test scores of 32 students are listed below. Find $\mathrm { P } _ { 46 }$ . $\begin{array} { l l l l l l l l } 32 & 37 & 41 & 44 & 46 & 48 & 53 & 55 \end{array}$ $\begin{array} { l l l l l l l l } 56 & 57 & 59 & 63 & 65 & 66 & 68 & 69 \end{array}$ $\begin{array} { l l l l l l l l } 70 & 71 & 74 & 74 & 75 & 77 & 78 & 79 \end{array}$ $\begin{array} { l l l l l l l l } 80 & 82 & 83 & 86 & 89 & 92 & 95 & 99 \end{array}$

Construct a data set for which the range is misleading as a measure of variation. Explain why the range is misleading and suggest an alternative measure of variation.

Does the mode of a numerical data set always lie close to the median? Explain your answer and give an example of a data set to illustrate your answer.

The signal-to-noise ratio of a set of data is obtained by dividing the mean by the standard deviation. Find the signal-to-noise ratio for the following sample of weights (in pounds) : $\begin{array} { l l l l l } 160 & 123 & 186 & 105 & 197 \\120 & 172 & 157 & 116 & 125\end{array}$

Find the mode(s) for the given sample data. - $\begin{array} { l l l l l l l } - 20 & - 45 & - 46 & - 45 & - 49 & - 45 & - 49 \end{array}$ A) $- 46$ B) $- 45$ C) $- 42.7$ D) $- 49$

In the Florida lottery, the numbers (between 1 and 49) are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

Find the midrange for the given sample data. -A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown below. Find the midrange. $\begin{array} { r r r r r r r } 72 & 143 & 52 & 84 & 100 & 98 & 101 \\120 & 99 & 121 & 86 & 60 & 59 & 71 \\125 & 130 & 104 & 74 & 83 & 55 & 169\end{array}$

Find the mean and median for each of the two samples, then compare the two sets of results. -The Body Mass Index (BMI) is measured for a random sample of men from two different colleges. Interpret the results by determining whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If there is, what is it? $\begin{array} { l | c | c | c | c | c | c | c | c } \text { Baxter College } & 24 & 23.5 & 22 & 27 & 25 & 21.5 & 25 & 24 \\\hline \text { Banter College } & 19 & 20 & 24 & 25 & 31 & 18 & 29 & 28\end{array}$