6B

According to the video, what was the range rule of thumb estimate for the standard deviation for Best Bank? Choose the correct answer below.

0.675

Using the range rule of thumb, what was the range of gas mileage for the Malibu Hybrid, as seen in the video? Choose the correct answer below.

41 to 57

Describe the process of calculating a standard deviation. Give a simple example of its calculation (such as calculating the standard deviation of the numbers 2,3,4,4, and 6). What is the standard deviation if all of the sample values are the same? Fill in the blanks to complete the process of calculating a standard deviation.

Compute the mean of the data set. Then find the deviation from the mean for every data value by subtracting the mean from the data value. Find the squares of all the deviations from the mean, and then add them together. Divide the sun by the total number of data values minus 1. The standard deviation is the square root of this quotient. The standard deviation of the numbers 2,3,4,4, and 6 is approximately 1.483. If all of the sample values are the same, then the standard deviation is 0.

What type of distribution has a negative standard deviation? Choose the correct answer below.

None. The standard deviation cannot be negative, because each deviation from the mean is squared.

After recording the pizza delivery times for two pizza shops, you conclude that one pizza shop has a mean delivery time of 46 minutes with a standard deviation of 3 minutes. The other shop has a mean delivery time of 45 minutes with a standard deviation of 20 minutes. Interpret these figures. If you liked the pizzas from both shops equally well, which one would you order from? Why?

The means are nearly equal, but the variation is significantly greater for the second shop than for the first. Choose the first shop. The delivery time is more reliable because it has a lower standard deviation.

For 30 students who took the test, the high score was 80, the median was 75, and the low score was 40. Correct the correct answer below.

The statement makes sense because it is possible that when sorting the 30 scores from low to high, the first value was 40, the highest value was 80, and 75 was halfway between the 15th and the 16th score.

The standard deviation for the heights of a group of 5-year-old children is smaller than the standard deviation for the heights of a group of children who range in age from 3 to 15. Choose the correct answer below.

The statement makes sense because the range of data for the heights of a group of 5-year-old children is smaller than the range of data for the heights of a group of children who range in age from 3 to 15.

According to the video, which statement is what was the upper quartile of the second set of race times? Choose the correct answer below.

11.30

A report claims that the returns for the investment portfolios with a single stock have a standard deviation of 0.58, while the returns for portfolios with 35 stocks have a standard deviation of 0.331. Explain how the standard deviation measures the risk in these two types of portfolios. Choose the correct answer below.

A lower standard deviation means more certainly in the return and less risk. Hence, the returns for portfolios with 35 stocks have less risk than the ones with a single stock.

The lower quartile for wages at a coffee shop is $8.75, and the upper quartile is $10.75. What can you conclude? Choose the correct answer below.

Half the workers earn between $8.75 and $10.75, because the lower quartile has one-quarter of the workers below it while the upper quartile has three-quarters of the workers below it.

The years following the recession of 2009 saw much attention given to inflation. Two tools provide a balanced measure of inflation. They are the PPI (producer price index) and the CPI (consumer price index). During 2013, production prices for nonalcoholic beverages rose but consumer prices dropped slightly. As available supply of used cars on auto lots dropped, so did prices despite increased consumer interest. The U.S. experienced an overall inflation rate of 1.7% for the first half of 2013, a figure which the Federal Reserve watched closely when setting the central bank's interest rate. What kind of relationship is shown in the above example between the production price and the consumer price of nonalcoholic beverages in 2013?

Inverse variation

Consider two grocery stores at which the mean time in line is the same but the variation is different. At which store would you expect the customers to have more complaints about the waiting time? Explain. Choose the correct answer below.

The customers would have more complaints about the waiting time at the store that has more variation because some customers would have longer waits and might think they are being treated unequally.

Find the mean and median for the waiting times at Big Bank given below. Show your work clearly, and verify that both are the same. The following values are measured in minutes. Big Bank: 4.1 5.2 5.6 6.2 6.7 7.2 7.7 7.7 8.5 9.3 11.0 Calculate the mean.

The mean is 7.2. Notice that the data are given in ascending order. How should the median be found in this case? Select the correct choice below and fill in the answer box(es) to complete your choice. The median is the 6th value in the sorted data set. Thus, the median is 7.2. The mean is equal to the median.

A small animal veterinarian reviews her records for the day and notes that she has seen eight dogs and eight cats with the following weights (in pounds). Dogs: 12,23,38,43,51,62,75,101. Cats: 5,5,6,8,11,16,18,23 a. Make correct conjectures about which set has the larger mean, median, and standard deviation. Choose the correct answer below. b. Compute the mean and standard deviation of each set.

The mean, median, and standard deviation are all higher for dogs because most of the weights are larger, so the average value, middle value, and spread must be larger. The mean for the dogs is 50.6. The mean for the cats is 11.5. The standard deviation for the dogs is 28.6. The standard deviation for the cats is 6.8.

What are the quartiles of a distribution? How do we find them?

The quartiles are values that divide the data distribution into quarters. The lower quartile is the median of the data values in the lower half of a data set. The middle quartile is the overall median. The upper quartile is the median of the data values in the upper half of data set.

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Choose the correct answer below.

This does not make sense because the range is the difference between the highest and lowest data values. It has nothing to do with the median.

An auto transmission manufacturer receives ball bearings from two different suppliers. The ball bearings must have a specified diameter of 16.30 mm with a tolerance of +-0.1 mm. Recent shipments from the two suppliers had ball bearings with the following diameters. Complete parts (a) through (c). Supplier A: 16.23,16.25,16.31,16.34,16.38,16.41,16.44 Supplier B: 16.18,16.21,16.24,16.33,16.37,16.41,16.46

a. Find the mean and standard deviation for each of the two data sets. Find the mean and standard deviation for the diameters of the ball bearings from Supplier A. mean= 16.34 s= 0.08 Find the mean and standard deviation for the diameters of the ball bearings from Supplier B. mean= 16.31 s= 0.11 b. Draw a box plot for each data set, and mark the tolerance on each box plot. Supplier AC. : —— : :|-| | :-| : ——- : Supplier B B. : —— — : |- :| | :|- : —— - : c. What percentage of ball bearings from each supplier meet specifications? Find the percentage of ball bearings from Supplier A that meet specifications. 71% Find the percentage of ball bearings from Supplier B that meet specifications. 57%

The table to the right gives the cost of living index (COLI) for six East Coast counties and six Midwest counties (using an index where 100 represents the average cost of living for all participating cities with a population of more than 1.5 million). Answer parts (a) through (e) below.

a. Find the mean, median, and range for each of the two data sets. The mean for the East Coast Counties is 157.82. The median for the East Coast Counties is 131.4. The range for the East Coast Counties is 209.4. The mean for the Midwest Counties is 115.87. The median for the Midwest Counties is 95. The range for the Midwest Counties is 141.7. b. Give the five-number summary and draw a box plot for each of the two data sets. Give the five-number summary and draw a box plot for the East Coast Counties. Low value= 104.8,Lower quartile= 123.2 Median= 131.4, Upper quartile=141.9 High value= 314.2. Choose the correct box plot for the East Coast Counties below. A.|—|-|-|—————-| Give the five-number summary for the Midwest Counties below. Low value= 87.1, Lower quartile= 92.7 Median= 95, Upper quartile= 96.6 High value= 228.8 Choose the correct box plot for the Midwest Counties below. A. |-||||————————-| c. Find the standard deviation for each of the two data sets. The standard deviation for the East Coast Counties is 77.63. The standard deviation for the Midwest Counties is 55.43. d. Apply the range rule of thumb to estimate the standard deviation of each of the two data sets. How well does the rule work in each case? Briefly discuss why it does or does not work well. The standard deviation for the East Coast Counties is approximately 52.35, using the range rule of thumb. The standard deviation for the Midwest Counties is approximately 35.43, using the range rule of thumb. How well does the rule work in each case? Briefly discuss why it does or does not work well. Choose the correct answer below. They do not work well in both of the two data sets because there are outliers of the two data sets. e. Based on all the results, compare and discuss the two data sets in terms of their center and variation. Choose the correct answer below. Select all that apply. The variation of COLI for the six East Coast Counties is higher than that for the six Midwest Counties, which means the level of COLI in most Midwest Counties varies in a smaller range. The mean of COLI for the six East Coast Counties is higher than that for the six Midwest Counties, which means the average level of COLI for the East Coast Counties is higher.

The table below shows the fraction of games won (to the nearest thousandth) by six professional teams in the east coast and west coast leagues for the 2016 season. The lists include the teams with the best and worst win-loss records in both leagues. Complete parts (a) through (e) below. East coast teams: 0.419,0.454,0.487,0.547,0.594,0.632 West coast teams: 0.369,0.411,0.500,0.571,0.585,0.588

a. Find the mean, median, and range for each of the two data sets. The mean for the east coast teams is 0.522. The median for the east coast is 0.517. The range for the east coast teams is 0.213. The mean for the west coast teams is 0.504. The median for the west coast teams is 0.536. The range for the west coast teams is 0.219. b. Give the five-number summary and draw a box plot for each of the data sets. Complete the five-number summary for the east coast teams. Lowest value Lower quartile. Median. Upper. Highest 0.419,0.454,0.517,0.594,0.632 Choose the correct box plot for the east coast teams below. C. — — |-|. |. |-| Complete the five-number summary for the west coast teams. Lowest value. Lower quartile. Median Upper quartile Highest value 0.369,0.411,0.536,0.585,0.588 Choose the correct box plot for the west coast teams below. B. ——- - |—|. |. || c. Find the standard deviation for each of the data sets. The standard deviation for the east coast teams is 0.083. The standard deviation for the west coast teams is 0.095. d. Apply the range rule of thumb the standard deviation for the east coast teams is approximately 0.053. Using the range rule of thumb the standard deviation for the west coast teams is approximately 0.055. How well does the rule work in each case? The rule does not work well in both of the data sets because the data is not distributed evenly. e. Based on all your results, compare and discuss the two data sets in terms of their center and variation. The mean is higher for the east coast teams, therefore the center of the data is larger for east coast teams. The standard deviation is higher for the west coast teams, therefore the variation is larger for west coast teams.

The accompanying data set gives the number of exercise hours per week and the number of TV hours per week of 50 college students l. Use StatCrunch to complete parts (a) through (d) below. Click the icon to view the college student data.

a. Find the range and standard deviation of the hours spent exercising per week. The range of hours exercising per week is 35 hours. The standard deviation spent exercising per week is 8.08 hours. b. Find the range and standard deviation of the hours spent watching TV per week. The range of hours spent watching TV per week is 15 hours. The standard deviation of hours spent watching TV per week is 3.89 hours. c. Make a box plot of the exercise data set grouped by year. The result will be separate box plots for first-year students, sophomores, juniors, and seniors. Choose the correct box plots below. Click here to view box plot set d. Common on the results. From these boxplots, it seems like the variation in exercise amount decreases as students progress through college. However, this variation could very well be explained by having fewer data points in the later years. d. Make a box plot of the data for TV hours per week grouped by handedness. The result will be separate box plots for right- and left-handed students. Choose the correct box plots below. Click here to view the box plots for choice a. Common on the results. While the box plots aren't perfectly identical, they have similar ranges and interquartile ranges. Thus, it seems like the amount of time spent watching TV varies a lot regardless of handedness.