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Organizing Data Solved Problems for Beginning Statistics

By — McGraw-Hill Professional
Updated on Apr 25, 2014

Review the following concepts if necessary:

Raw Data

  1. Classify the following data as either qualitative data or quantitative data. In addition, classify the quantitative data as discrete or continuous.
    1. The number of times that a movement authority is sent to a train from a relay station is recorded for several trains over a two-week period. The movement authority, which is an electronic transmission, is sent repeatedly until a return signal is received from the train.
    2. A physician records the follow-up condition of patients with optic neuritis as improved, unchanged, or worse.
    3. A quality technician records the length of material in a roll product for several products selected from a production line.
    4. The Bureau of Justice Statistics Sourcebook of Criminal Justice Statistics in reporting on the daily use within the last 30 days of drugs among young adults lists the type of drug as marijuana, cocaine, or stimulants (adjusted).
    5. The number of aces in five-card poker hands is noted by a gambler over several weeks of gambling at a casino.

      Ans.

      1. The number of times that the moving authority must be sent is countable and therefore these data are quantitative and discrete.
      2. These data are categorical or qualitative.
      3. The length of material can be any number within an interval of values, and therefore these data are quantitative and continuous.
      4. These data are categorical or qualitative
      5. Each value in the data set would be one of the five numbers 0, 1, 2, 3, or 4. These data are quantitative and discrete.

Frequency Distribution for Qualitative Data

Give a frequency distribution for these data.

Ans.     The academic ranks are tallied into the four possible categories and the results are shown in Table 2.13.

  1. The following list gives the academic ranks of the 25 female faculty members at a small liberal arts college:

Relative Frequency of a Category and Percentage

Ans.     Each frequency in Table 2.13 is divided by 25 to obtain the relative frequencies for the categories. The relative frequencies are then multiplied by 100 to obtain percentages. The results are shown in Table 2.14.

  1. Give the relative frequencies and percentages for the categories shown in Table 2.13.
  2. Refer to Table 2.14 to answer the following.
    1. What percent of the female faculty have a rank of associate professor or higher?
    2. What percent of the female faculty are not full professors?
    3. What percent of the female faculty are assistant or associate professors?

      Ans.

      1. 24% + 12% = 36%
      2. 16% + 48% + 24% = 88%
      3. 48% + 24% = 72%

Bar Graphs and Pie Charts

Ans.   The Excel horizontal bar graph for the distribution given in Table 2.15 is shown in Fig. 2-9.

Organizing Data Solved Problems

Ans.   Table 2.16 illustrates the determination of the angles for each sector of the pie chart.

The Excel pie chart for the distribution given in Table 2.15 is shown in Fig. 2-10.

Organizing Data Solved Problems

Organizing Data Solved Problems

  1. The subjects in an eating disorders research study were divided into one of three different groups. Table 2.15 gives the frequency distribution for these three groups. Construct a bar graph.
  2. Construct a table showing the relative frequency and the size of the angles for the frequency distribution given in Table 2.15. Also use Excel to construct a pie chart.
  3. A survey of 500 randomly chosen individuals is conducted. The individuals are asked to name their favorite sport. The STATISTIX pie chart in Fig. 2-11 summarizes the results of this survey.
    1. How many individuals in the 500 gave baseball as their favorite sport?
    2. How many gave a sport other than basketball as their favorite sport?
    3. How many gave hockey or golf as their favorite sport?

      Ans.

      1. .3 × 500 = 150
      2. .8 × 500 = 400
      3. .2 × 500 = 100
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