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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
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In a recent issue of the IEEE Spectrum , 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

  • Organize the data in a chart.
  • Find the median, the first quartile, and the third quartile.
  • Find the 65th percentile.
  • Find the 10th percentile.
  • Construct a box plot of the data.
  • The middle 50% of the conferences last from _______ days to _______ days.
  • Calculate the sample mean of days of engineering conferences.
  • Calculate the sample standard deviation of days of engineering conferences.
  • Find the mode.
  • If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.
  • Give two reasons why you think that 3 - 5 days seem to be popular lengths of engineering conferences.
  • 4,3,5
  • 4
  • 3
  • A box plot with a whisker between 2 and 3, a solid line at three, a dashed line at 4, a solid line at 5, and a whisker between 5 and 9.
  • 3,5
  • 3.94
  • 1.28
  • 3
  • mode
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A survey of enrollment at 35 community colleges across the United States yielded the following figures ( source: Microsoft Bookshelf ):

  • 6414
  • 1550
  • 2109
  • 9350
  • 21828
  • 4300
  • 5944
  • 5722
  • 2825
  • 2044
  • 5481
  • 5200
  • 5853
  • 2750
  • 10012
  • 6357
  • 27000
  • 9414
  • 7681
  • 3200
  • 17500
  • 9200
  • 7380
  • 18314
  • 6557
  • 13713
  • 17768
  • 7493
  • 2771
  • 2861
  • 1263
  • 7285
  • 28165
  • 5080
  • 11622

  • Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment"and "Frequency."
  • Construct a histogram of the data.
  • If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
  • Calculate the sample mean.
  • Calculate the sample standard deviation.
  • A school with an enrollment of 8000 would be how many standard deviations away from the mean?
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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
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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
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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