Exam 3: Numerically Summarizing Data

Use Chebyshev s Inequality to Describe Any Set of Data -If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean

The repair costs for five cars which were crashed by a safety testing organization were as follows: $\$ 130 , \$ 140 , \$ 190 , \$ 230$ , and $\$ 140$ . Find the mean cost of repair.

Use Chebyshev s Inequality to Describe Any Set of Data -Commuting times for employees of a local company have a mean of 63.6 minutes and a standard deviation of 2.5 minutes. What does Chebyshev s Theorem say about the percentage of employees with commuting times between 58.6 minutes and 68.6 minutes

Draw and Interpret Boxplots -The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Draw a boxplot that represents the data. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 275

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

Use Chebyshev s Inequality to Describe Any Set of Data -At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 99 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player s serves.

Determine the Mode of a Variable from Raw Data -The February utility bills (in dollars) for ten residents of a large city are listed below. Find the mode amount. 71 67 67 72 76 72 73 68 72 72

Provide an appropriate response. -Describe the shape of the histogram. The data set: age of 20 household stereo systems randomly selected from a neighborhood 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1

Provide an appropriate response. -Given the following five-number summary, find Q3. 2.9, $\quad 5.7 , \quad 10.0 , \quad 13.2 , \quad 21.1$ .

Determine the Mode of a Variable from Raw Data -Calculate the mean, median, and mode for the following sample: $5,10,6,100,0,0,10,0$

Compute the Standard Deviation of a Variable from Raw Data -8, 7, 7, 7, 12, 11, 14, 16, 14

Provide an appropriate response. -For the following data, approximate the mean weekly grocery bill. Bill (in dollars) Frequency 135-139 17 140-144 14 145-149 6 150-154 8 155-159 11

Determine the Mode of a Variable from Raw Data -The accompanying data set contains quiz scores for 12 students in a chemistry class: $18,15,5,8,15,20,2,16,10 \text {, }$ $12,20,15$ a. Find a measure of central tendency that separates the data into two groups such that each group consists of 50% of the scores above and 50% of the scores below that measure. b. Find a measure of central tendency that represents the quiz score that occurs most often. c. Find a measure of central tendency that represents the average of the 12 quiz scores.

Use the Empirical Rule to Describe Data That Are Bell Shaped -The average score of local students on a college entrance exam is 110 , with a standard deviation of 5 . The distribution is roughly bell shaped. Use the Empirical Rule to find the percentage of local students with scores above 120 .

Provide an appropriate response. -A statistic is said to be biased if it

Use Chebyshev s Inequality to Describe Any Set of Data -Fill in the blank. ____________ gives us a method of interpreting the standard deviation that applies to any data set, regardless of the shape of the distribution.

Provide an appropriate response. -For the data set given below the sample variance will be computed. How many degrees of freedom are there 6 9 6 1 5 11 5 9 8

Compute the Standard Deviation of a Variable from Raw Data -3, 3, 14, 11, 11, 20, 14, 10, 14

Compute the Standard Deviation of a Variable from Raw Data -The costs (in dollars) of 10 college math textbooks are listed below. Find the sample standard deviation. 70 72 71 70 69 73 69 68 70 71

Compute the Range of a Variable from Raw Data - $0.126,0.12,0.547,0.414,0.636,0.309$