Question

students at a major university in southern california are complaining about a serious housing crunch. they are stating that many of them have to commute too far to school because there is not enough housing near campus. the university officials’ response is to perform a study, reported in the school newspaper, contains the following histogram summarizing the commute distances for a sample of 100 students at the university.
histogram: y - axis (relative frequency) with values 0.00, 0.10, 0.20, 0.30; x - axis (commute distance in miles) with intervals 0–4, 4–8, 8–12, 12–16, 16–20, 20–24. bar heights: 0–4: 0.26, 4–8: 0.26, 8–12: 0.18, 12–16: 0.14, 16–20: 0.11, 20–24: 0.05
based on this histogram, draw the ogive (the cumulative relative frequency polygon) for the data in the study.
ogive plot area: y - axis (cumulative relative frequency) with values 0, 0.2, 0.4, 0.6, 0.8, 1; x - axis (commute distance in miles) with points at 0, 4, 8, 12, 16, 20, 24 labeled 0.00

Explanation:

Step1: Calculate cumulative relative frequency for 4 miles

Cumulative relative frequency at 4 miles is the relative frequency of 0 - 4 miles, which is 0.26.

Step2: Calculate cumulative relative frequency for 8 miles

Add relative frequency of 4 - 8 miles (0.26) to previous cumulative: \(0.26 + 0.26 = 0.52\)

Step3: Calculate cumulative relative frequency for 12 miles

Add relative frequency of 8 - 12 miles (0.18) to previous cumulative: \(0.52 + 0.18 = 0.70\)

Step4: Calculate cumulative relative frequency for 16 miles

Add relative frequency of 12 - 16 miles (0.14) to previous cumulative: \(0.70 + 0.14 = 0.84\)

Step5: Calculate cumulative relative frequency for 20 miles

Add relative frequency of 16 - 20 miles (0.11) to previous cumulative: \(0.84 + 0.11 = 0.95\)

Step6: Calculate cumulative relative frequency for 24 miles

Add relative frequency of 20 - 24 miles (0.05) to previous cumulative: \(0.95 + 0.05 = 1.00\)

To draw the ogive, plot the points (0, 0.00), (4, 0.26), (8, 0.52), (12, 0.70), (16, 0.84), (20, 0.95), (24, 1.00) and connect them with straight lines.

Answer:

The ogive is drawn by plotting points (0, 0.00), (4, 0.26), (8, 0.52), (12, 0.70), (16, 0.84), (20, 0.95), (24, 1.00) and connecting them.