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Exam 3: Numerically Summarizing Data

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Question 31

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The output below gives the mean and median for the national dropout rates of high school students in 2010and 2012. $\begin{array} { l r r } & \text { Drop 2010 } & \text { Drop 2012 } \\\text { N } & 51 & 51 \\\text { MEAN } & 28.38 & 26.76 \\\text { MEDIAN } & 27.94 & 25.54\end{array}$ 51Use the sample information to determine the shape of the distributions of the high school dropout rates in 2010and 2012.

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In both 2010 and 2012, the mea...

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Question 32

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The graph below is an ogive of scores on a math test. The vertical axis in an ogive is the cumulative relativefrequency and can also be interpreted as a percentile. Use the graph to approximate the test score that corresponds to the 40th percentile?

A) 62
B) 10
C) 56
D) 15

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Question 33

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Over the last 10 years four mutual funds all had the same mean rate of return, 12%. These mutual funds haddifferent standard deviations as follows: Mutual Money 8%, Co-joined Investments 6%, Together Fund 4%, Allfor One Fund 9%. Which mutual fund investment is the most consistent in rate of return?

The number of students enrolled in a physics class for the last ten semesters are listed below. Find the mediannumber of students.65 66 67 66 67 70 67 70 71 68

A survey of 200 public universities indicated that the 25th percentile of the yearly tuition cost of the universitieswas $4400 and the 75th percentile was $7000. The minimum value was $2000, the median was $6000, and themaximum was $10,000. Use this information to construct a boxplot for the yearly tuition costs.

For the following data set, approximate the sample standard deviation of unused vacation days . $\begin{array} { c | c } \text { Days } & \text { Frequency } \\\hline 1 - 2 & 9 \\3 - 4 & 22 \\5 - 6 & 28 \\7 - 8 & 15 \\9 - 10 & 14\end{array}$

When results from a scholastic assessment test are sent to test-takers, the percentiles associated with theirscores are also given. Suppose a test-taker scored at the 99th percentile for their verbal grade and at the 36thpercentile for their quantitative grade. Interpret these results.

8, 19, 2, 13, 9

The following is a sample of 19 November utility bills (in dollars) from a neighborhood.What is the largest billin the sample that would not be considered an outlier?52, 62, 66, 68, 72, 74, 76, 76, 76, 78, 78, 82, 84, 84, 86, 88, 92, 96, 110

Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare thecost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution ofthe amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $120and a standard deviation of $11. If the distribution can be considered bell shaped, what percentage of homeswill have a monthly utility bill of more than $109?

Given the following five-number summary, find the interquartile range.29, 37, 50, 66, 94

The _______________ is the easiest measure of dispersion to calculate.

9, 9, 7, 1, 6, 10, 9, 7, 9

The average score of local students on a college entrance exam is 110, with a standard deviation of 5. Thedistribution is roughly bell shaped. Use the Empirical Rule to find the percentage of local students with scoresabove 120.

Which measure of central tendency may have more than one value in a numeric data set?

The annual profits of five large corporations in a certain area are given below. Which measure of centraltendency should be used?$135,000 $143,000 $163,000 $133,000 $1,213,000

The ________ of a variable is computed by determining the sum of all the values of the variable in the data setand dividing this sum by the number of observations in the data set.

Many firms use on-the-job training to teach their employees new software. Suppose you work in the personneldepartment of a firm that just finished training a group of its employees in new software, and you have beenrequested to review the performance of one of the trainees on the final test that was given to all trainees. Themean and standard deviation of the test scores are 73 and 2, respectively, and the distribution of scores ismound-shaped and symmetric. Suppose the trainee in question received a score of 72. Compute the traineeʹsz-score.

For the following data set, approximate the sample standard deviation of distances from work (in miles) . $\begin{array} { c | c } \text { Distance(miles) } & \text { Frequency } \\\hline 8 - 11 & 15 \\12 - 15 & 21 \\16 - 19 & 36 \\20 - 23 & 39 \\24 - 27 & 23\end{array}$

The monthly telephone usage (in minutes) of 30 adults is listed below. Find the interquartile range for thetelephone usage of the 30 adults. $\begin{array} { l l l l l l l l l l } 154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \\189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \\205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265\end{array}$