33. student loans on the rise: percentage of bachelors degree recipients with federal student loans and…

33. student loans on the rise: percentage of bachelors degree recipients with federal student loans and median loan amount 1992 - 93 36.8% $10,008 1995 - 96 50.1% $13,327 1999 - 00 60.3% $16,858 2003 - 04 63.0% $18,432 source: american council on education * writing in mathematics 34. what is a population? what is a sample? 35. describe what is meant by a random sample. 36. suppose you are interested in whether or not the students at your college would favor a grading system in which stu - dents may receive final grades of a +, a, a -, b +, b, b -, c +, c, c -, and so on. describe how you might obtain a random sample of 100 students from the entire student population. 37. for exercise 36, would questioning every fifth student as he or she is leaving the campus library until 100 students are interviewed be a good way to obtain a random sample? explain your answer. 38. what is a frequency distribution? 39. what is a histogram? 40. what is a frequency polygon? 41. describe how to construct a frequency polygon from a histogram. 42. describe how to construct a stem - and - leaf plot from a set of data. 43. describe two ways that graphs can be misleading. * critical thinking exercises 44. construct a grouped frequency distribution for the following data, showing the length, in miles, of the 25 longest rivers in the united states. use five classes that have the same width. 2540 2340 1980 1900 1460 1450 1420 1310 1290 1280 1240 1040 990 926 906 886 862 800 774 743 724 692 659 649 source: u.s. department of the interior 45. use two line graphs drawn in the same coordinate system that show a better way to portray the enrollment information for 2000 through 2004 in exercise 42. * group exercises 46. the classic book on statistical distortion using statistics is how to lie with statistics by darrell huff. this activity is designed for five people. each person should select two chapters from huffs book and then present to the class the two methods of statistical manipulation and the common that huff discusses. 47. each group member should find one example of a graph that presents data with integrity and one example of a graph that is misleading. use newspapers, magazines, the internet, books, and so forth. once graphs have been col - lected, each member should share his or her graphs with the entire group. be sure to explain why one graph depicts data in a forthright manner and how the other graph misleads the viewer.

33. student loans on the rise: percentage of bachelors degree recipients with federal student loans and median loan amount 1992 - 93 36.8% $10,008 1995 - 96 50.1% $13,327 1999 - 00 60.3% $16,858 2003 - 04 63.0% $18,432 source: american council on education * writing in mathematics 34. what is a population? what is a sample? 35. describe what is meant by a random sample. 36. suppose you are interested in whether or not the students at your college would favor a grading system in which stu - dents may receive final grades of a +, a, a -, b +, b, b -, c +, c, c -, and so on. describe how you might obtain a random sample of 100 students from the entire student population. 37. for exercise 36, would questioning every fifth student as he or she is leaving the campus library until 100 students are interviewed be a good way to obtain a random sample? explain your answer. 38. what is a frequency distribution? 39. what is a histogram? 40. what is a frequency polygon? 41. describe how to construct a frequency polygon from a histogram. 42. describe how to construct a stem - and - leaf plot from a set of data. 43. describe two ways that graphs can be misleading. * critical thinking exercises 44. construct a grouped frequency distribution for the following data, showing the length, in miles, of the 25 longest rivers in the united states. use five classes that have the same width. 2540 2340 1980 1900 1460 1450 1420 1310 1290 1280 1240 1040 990 926 906 886 862 800 774 743 724 692 659 649 source: u.s. department of the interior 45. use two line graphs drawn in the same coordinate system that show a better way to portray the enrollment information for 2000 through 2004 in exercise 42. * group exercises 46. the classic book on statistical distortion using statistics is how to lie with statistics by darrell huff. this activity is designed for five people. each person should select two chapters from huffs book and then present to the class the two methods of statistical manipulation and the common that huff discusses. 47. each group member should find one example of a graph that presents data with integrity and one example of a graph that is misleading. use newspapers, magazines, the internet, books, and so forth. once graphs have been col - lected, each member should share his or her graphs with the entire group. be sure to explain why one graph depicts data in a forthright manner and how the other graph misleads the viewer.

Answer

Explanation:

Step1: Identify the questions

We have multiple questions related to statistics concepts such as frequency distribution, histogram, frequency polygon, stem - and - leaf plot, population, sample, etc.

Step2: Analyze each question

For example, for question 38 "What is a frequency distribution?": A frequency distribution is a table that shows the number of times each value or range of values (class) occurs in a data - set. For question 39 "What is a histogram?": A histogram is a graphical representation of a frequency distribution. It consists of adjacent rectangles where the horizontal axis represents the class intervals and the vertical axis represents the frequencies. For question 40 "What is a frequency polygon?": A frequency polygon is a line graph that is formed by connecting the mid - points of the tops of the bars in a histogram or by plotting the mid - points of class intervals against their frequencies and then connecting the points with straight lines.

Step3: Answer construction

We will answer each question one by one. 38. A frequency distribution is a tabular arrangement that shows the number of observations falling into each of several non - overlapping classes. 39. A histogram is a bar graph of a frequency distribution where the horizontal axis represents classes of data values and the vertical axis represents frequencies, and the bars are adjacent. 40. A frequency polygon is a line graph obtained by plotting the mid - points of class intervals on the horizontal axis and their corresponding frequencies on the vertical axis and then connecting the points with line segments. 41. To construct a frequency polygon from a histogram: First, find the mid - points of the tops of the bars in the histogram. Then, plot these mid - points on a graph with the class mid - points on the x - axis and the frequencies on the y - axis. Finally, connect the points with straight lines. 42. To construct a stem - and - leaf plot from a set of data: Separate each data value into a stem and a leaf. The stem is the leading digit(s) and the leaf is the trailing digit. List the stems in a vertical column. For each data value, write the leaf in the row corresponding to its stem. 43. Graphs can be misleading in several ways. For example, using a non - zero origin on the vertical axis can exaggerate differences. Also, distorting the scale or using 3D effects inappropriately can mislead the viewer. 44. To construct a grouped frequency distribution for the given data: First, determine the range of the data (the difference between the maximum and minimum values). Then, decide on the number of classes and the class width. Tally the data into the classes and count the frequencies. 45. To use two line graphs in the same coordinate system to show enrollment from 2000 - 2004: Label the x - axis as the years (2000, 2001, 2002, 2003, 2004) and the y - axis as the enrollment. Plot two different lines, one for each data set related to enrollment, using different colors or line styles to distinguish them. 46. Each person in the group should read the assigned chapters from "How to Lie with Statistics" by Darrell Huff, discuss the statistical manipulation and distortion methods, and then present to the class. 47. Each group member should find a graph with integrity (showing data accurately) and a misleading graph. Present them to the group, explaining how the misleading graph misleads the viewer and how the other graph presents data in a forthright manner.

Answer:

  1. A frequency distribution is a tabular arrangement that shows the number of observations falling into each of several non - overlapping classes.
  2. A histogram is a bar graph of a frequency distribution where the horizontal axis represents classes of data values and the vertical axis represents frequencies, and the bars are adjacent.
  3. A frequency polygon is a line graph obtained by plotting the mid - points of class intervals on the horizontal axis and their corresponding frequencies on the vertical axis and then connecting the points with line segments.
  4. To construct a frequency polygon from a histogram: First, find the mid - points of the tops of the bars in the histogram. Then, plot these mid - points on a graph with the class mid - points on the x - axis and the frequencies on the y - axis. Finally, connect the points with straight lines.
  5. To construct a stem - and - leaf plot from a set of data: Separate each data value into a stem and a leaf. The stem is the leading digit(s) and the leaf is the trailing digit. List the stems in a vertical column. For each data value, write the leaf in the row corresponding to its stem.
  6. Graphs can be misleading in several ways. For example, using a non - zero origin on the vertical axis can exaggerate differences. Also, distorting the scale or using 3D effects inappropriately can mislead the viewer.
  7. To construct a grouped frequency distribution for the given data: First, determine the range of the data (the difference between the maximum and minimum values). Then, decide on the number of classes and the class width. Tally the data into the classes and count the frequencies.
  8. To use two line graphs in the same coordinate system to show enrollment from 2000 - 2004: Label the x - axis as the years (2000, 2001, 2002, 2003, 2004) and the y - axis as the enrollment. Plot two different lines, one for each data set related to enrollment, using different colors or line styles to distinguish them.
  9. Each person in the group should read the assigned chapters from "How to Lie with Statistics" by Darrell Huff, discuss the statistical manipulation and distortion methods, and then present to the class.
  10. Each group member should find a graph with integrity (showing data accurately) and a misleading graph. Present them to the group, explaining how the misleading graph misleads the viewer and how the other graph presents data in a forthright manner.