Questions: Students at a major university in Southern California are complaining about a serious housing crunch. They are stating that many of the university's students have to commute too far to school because there is not enough housing near campus. The histogram summarizing the commute distances for a sample of 100 students at the university. Based on this histogram, draw the ogive (the cumulative relative frequency polygon) for the data in the study.

Students at a major university in Southern California are complaining about a serious housing crunch. They are stating that many of the university's students have to commute too far to school because there is not enough housing near campus. The histogram summarizing the commute distances for a sample of 100 students at the university. Based on this histogram, draw the ogive (the cumulative relative frequency polygon) for the data in the study.
Transcript text: Students at a major university in Southern California are complaining about a serious housing crunch. They are stating that many of the university's students have to commute too far to school because there is not enough housing near campus. The histogram summarizing the commute distances for a sample of 100 students at the university. Based on this histogram, draw the ogive (the cumulative relative frequency polygon) for the data in the study.
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Solution

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Solution Steps

Step 1: Calculate the cumulative relative frequencies

The cumulative relative frequency is the sum of the relative frequencies up to a specific data point. We can calculate these values based on the histogram provided.

  • 0-4 miles: 0.21
  • 4-8 miles: 0.21 + 0.27 = 0.48
  • 8-12 miles: 0.21 + 0.27 + 0.19 = 0.67
  • 12-16 miles: 0.21 + 0.27 + 0.19 + 0.13 = 0.80
  • 16-20 miles: 0.21 + 0.27 + 0.19 + 0.13 + 0.12 = 0.92
  • 20-24 miles: 0.21 + 0.27 + 0.19 + 0.13 + 0.12 + 0.06 = 0.98
Step 2: Plot the cumulative relative frequencies

The Ogive graph plots the cumulative relative frequency at the upper limit of each interval's bin. Plot the following points, using the upper class boundaries as x-values and the cumulative relative frequencies as y-values:

  • (4, 0.21)
  • (8, 0.48)
  • (12, 0.67)
  • (16, 0.80)
  • (20, 0.92)
  • (24, 0.98)

Also include the point (0,0) as the ogive always starts at zero. Draw a line from (0,0) and connecting the other calculated points.

Step 3: Verify with the given ogive

The points and the line you plotted in step 2 should perfectly match the empty circles connected by the line in the ogive provided in the original image.

Final Answer:

The final answer is the completed ogive (cumulative relative frequency polygon) as provided in the original image with all the empty points plotted as described in Step 2.

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