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Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all on-board transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Below is a summary of the bills for each group.

Singles
Amount($) Frequency Rel. Frequency
51-100 5
101-150 10
151-200 15
201-250 15
251-300 10
301-350 5
Couples
Amount($) Frequency Rel. Frequency
100-150 5
201-250 5
251-300 5
301-350 5
351-400 10
401-450 10
451-500 10
501-550 10
551-600 5
601-650 5
  • Fill in the relative frequency for each group.
  • Construct a histogram for the Singles group. Scale the x-axis by $50. widths. Use relative frequency on the y-axis.
  • Construct a histogram for the Couples group. Scale the x-axis by $50. Use relative frequency on the y-axis.
  • Compare the two graphs:
    • List two similarities between the graphs.
    • List two differences between the graphs.
    • Overall, are the graphs more similar or different?
  • Construct a new graph for the Couples by hand. Since each couple is paying for two individuals, instead of scaling the x-axis by $50, scale it by $100. Use relative frequency on the y-axis.
  • Compare the graph for the Singles with the new graph for the Couples:
    • List two similarities between the graphs.
    • Overall, are the graphs more similar or different?
  • By scaling the Couples graph differently, how did it change the way you compared it to the Singles?
  • Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person in a couple? Explain why in one or two complete sentences.

Refer to the following histograms and box plot. Determine which of the following are true and which are false. Explain your solution to each part in complete sentences.

Three graphs; the first is a histogram with a mode of 3 and fairly symmetrical distribution between 1 (minimum value) and 5 (maximum value); the second is a histogram with peaks at 1 (minimum value) and 5 (maximum value) with 3 having the lowest frequency; the third is a box plot with data between 0 and a value greater than 6, Q1 at 1, M at 3, and Q3 at 6.
  • The medians for all three graphs are the same.
  • We cannot determine if any of the means for the three graphs is different.
  • The standard deviation for (b) is larger than the standard deviation for (a).
  • We cannot determine if any of the third quartiles for the three graphs is different.
  • True
  • True
  • True
  • False

Refer to the following box plots.

Two box plots showing data between 0 and 7.  The Data 1 box plot shows Q1 at 2, M at 4, and Q3 at some unlabeled point greater than 4, while the Data 2 plot shows Q1 at an unlabeled point between 0 and 2, M at 2, and Q3 slightly greater than 2.
  • In complete sentences, explain why each statement is false.
    • Data 1 has more data values above 2 than Data 2 has above 2.
    • The data sets cannot have the same mode.
    • For Data 1 , there are more data values below 4 than there are above 4.
  • For which group, Data 1 or Data 2, is the value of “7” more likely to be an outlier? Explain why in complete sentences

The median age of the U.S. population in 1980 was 30.0 years. In 1991, the median age was 33.1 years. ( Source: Bureau of the Census )

  • What does it mean for the median age to rise?
  • Give two reasons why the median age could rise.
  • For the median age to rise, is the actual number of children less in 1991 than it was in 1980? Why or why not?
  • Maybe

A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.

Three box plots on a chart scaled from less than 25 to 80.  The BMW 3 series plot shows a minimum value under 25, Q1 around 30, M around 34, Q3 around 41, and a maximum value near 66.  The BMW 5 series plot shows a minimum value around 31, Q1 around 40, M around 41, Q3 around 55, and a maximum value around 64,  The BMW 7 series plot show a mimimum value around 35, Q1 around 41, M around 46, Q3 around 59, and a maximum value around 68.
  • In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.
  • Which group is most likely to have an outlier? Explain how you determined that.
  • Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?
  • Look at the BMW 5 series. Which quarter has the smallest spread of data? What is that spread?
  • Look at the BMW 5 series. Which quarter has the largest spread of data? What is that spread?
  • Look at the BMW 5 series. Estimate the Inter Quartile Range (IQR).
  • Look at the BMW 5 series. Are there more data in the interval 31-38 or in the interval 45-55? How do you know this?
  • Look at the BMW 5 series. Which interval has the fewest data in it? How do you know this?
    • 31-35
    • 38-41
    • 41-64

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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Can you compute that for me. Ty
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Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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answer
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progressive wave
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Who can show me the full solution in this problem?
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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