Exam 3: Numerically Summarizing Data

Compute the Range of a Variable from Raw Data - $120,479,141,581,420,304$

Compute the Range of a Variable from Raw Data - $14,14,14,16,26,26,26$

Compute the Standard Deviation of a Variable from Raw Data -In a random sample, 10 employees at a local plant were asked to compute the distance they travel to work to the nearest tenth of a mile. The data is listed below. Compute the range, sample standard deviation and sample variance of the data. 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

Use the Empirical Rule to Describe Data That Are Bell Shaped -Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3 -bedroom house using gas or electric energy had a mean of $\$ 119$ and a standard deviation of $\$ 8$ . If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of more than $\$ 111$ ?

Compute the Standard Deviation of a Variable from Raw Data -Over the last 10 years four mutual funds all had the same mean rate of return, $12 \%$ . These mutual funds had different standard deviations as follows: Mutual Money 8\%, Co-joined Investments $6 \%$ , Together Fund $4 \%$ , All for One Fund $9 \%$ . Which mutual fund investment is the most consistent in rate of return?

Determine the Mode of a Variable from Raw Data -Find the mean, median, and mode of the following statistic students test scores: 100 103 96 100 93 101 100 94 95 98

Provide an appropriate response. -The ages of five randomly selected students in the biology department at a private university are 27, 26, 32, 18, and 19. Calculate the sample variance of these ages.

Determine the Median of a Variable from Raw Data -The number of yards that a football player rushed in the first 13 games of his NFL career are listed below. Find the mean and median number of yards rushed. Round the mean to the nearest whole number. Which measure of central tendency-the mean or the median-better represents the data Explain your reasoning. 3 49 32 33 39 22 42 9 9 39 52 58 70

Approximate the Variance and Standard Deviation of a Variable from Grouped Data -For the following data set, approximate the sample standard deviation of unused vacation days . Days Frequency 1-2 9 3-4 22 5-6 28 7-8 15 9-10 14

Approximate the Variance and Standard Deviation of a Variable from Grouped Data -For the following data set, approximate the sample standard deviation of distances from work (in miles). Distance(miles) Frequency 8-11 15 12-15 21 16-19 36 20-23 39 24-27 23

Provide an appropriate response. -Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 270 students and carefully recorded their parking times. The parking times recorded followed a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 270 student parking times collected.

Provide an appropriate response. -The output below gives the mean and median for the national dropout rates for high school students in 1982 and 1984. Drop 1982 Drop 1984 N 51 51 MEAN 28.66 26.58 MEDIAN 27.05 25.54 Use the sample information to determine the shape of the distributions of the high school dropout rates in 1982 and 1984.

Provide an appropriate response. -A student receives test scores of 62,83 , and 91 . The student's term project score is 88 and her homework score is 76. Each test is worth $20 \%$ of the final grade, the term project is $25 \%$ of the final grade, and the homework grade is $15 \%$ of the final grade. What is the student's mean score in the class?

Provide an appropriate response. -In distributions that are skewed to the right, what is the relationship of the mean, median, and mode

Determine and Interpret Quartiles -Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 70 75 68 78 88 76 63 91 67 92 71 94 78 64 83 65 70 83 70 75 68 78 88 76 63 91 67 92 71 94 78 64 83 65 70 83 72 75 62 89 77 66 84 72 75 62 89 77 66 84 Find $Q _ { 1 }$ of the data.

Provide an appropriate response. -The book cost (in dollars) for one semester's books are given below for a sample of five college students. Calculate the sample variance of the book costs. $280,120,405,485,325$

Determine the Mode of a Variable from Raw Data -The high temperatures (in degrees Celsius) each day over a three week period were as follows: 17,18 , 20, 22, $21,19,16,15,18,20,21,21,22,21,19,20,19,17,16,16,17$ . Compute the mean, median, and mode.

Determine and Interpret z-Scores -A pharmaceutical testing company wants to test a new cholesterol drug. The average cholesterol of the target population is 200 mg and they have a standard deviation of 25 mg. The company wished to test a sample of people who fall between 1.5 and 3 z-scores above the mean. Into what range must a candidate s cholesterol level be in order for the candidate to be included in the study

Provide an appropriate response. -On a recent day during the flu season, the Midtown Medical Clinic saw many patients. Patients had their temperatures (in °F) taken. The distribution of temperatures is given below. Determine the mean temperature of a sample of 100 patients. Temperatures Frequency 95.6-96.49 1 96.5-97.39 3 97.4-98.29 19 98.3-99.19 28 99.2-100.09 35 100.1-100.99 12 101.0-101.89 2

Provide an appropriate response. -In the computation of the sample standard variance, how many degrees of freedom are there in a data set that has 15 data values