Question

a transportation company owns 120 buses. the distance that each bus has travelled since being purchased by the company is recorded. the cumulative frequency curve for these data is shown. answer the following in spaces provided below. do not use spaces or commas. a. find the number of buses that travelled a distance between 15000 and 20000 kilometres. type your answer... b. use the cumulative frequency curve to find the median distance. type your answer... c. use the cumulative frequency curve to find the lower quartile. type your answer...

Explanation:

Step1: Find cumulative frequency at 15000 km

From the graph, cumulative - frequency at 15000 km is approximately 30.

Step2: Find cumulative frequency at 20000 km

From the graph, cumulative - frequency at 20000 km is approximately 90.

Step3: Calculate number of buses in the range

Number of buses = Cumulative frequency at 20000 km - Cumulative frequency at 15000 km = 90 - 30 = 60.

Step4: Find median

Since \(n = 120\), the median is the \(\frac{n + 1}{2}=\frac{120}{2}=60^{th}\) value. From the graph, the median distance is approximately 17500 km.

Step5: Find lower quartile

The lower quartile is the \(\frac{n}{4}=\frac{120}{4}=30^{th}\) value. From the graph, the lower - quartile distance is approximately 12500 km.

Answer:

a. 60
b. 17500
c. 12500