Question

a transportation company owns 30 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.
a. find the number of buses that travelled a distance between 25000 and 40000 kilometres.
20
b. use the cumulative frequency curve to find the median distance. 30000
c. use the cumulative frequency curve to find the lower quartile. 24000
d. use the cumulative frequency curve to find the upper quartile. 34000

Explanation:

Step1: Find cumulative frequencies at 25000 km and 40000 km

From the curve, cumulative - frequency at 25000 km is 10 and at 40000 km is 30.

Step2: Calculate number of buses in the range

Number of buses = Cumulative frequency at 40000 km - Cumulative frequency at 25000 km = 30 - 10=20.

Step3: Find the median

There are n = 30 buses. The median position is $\frac{n + 1}{2}=\frac{30+1}{2}=15.5$. Locate 15.5 on the cumulative - frequency axis and read off the distance on the x - axis, which is 30000 km.

Step4: Find the lower quartile

The lower - quartile position is $\frac{n + 1}{4}=\frac{30 + 1}{4}=7.75$. Locate 7.75 on the cumulative - frequency axis and read off the distance on the x - axis, which is 24000 km.

Step5: Find the upper quartile

The upper - quartile position is $\frac{3(n + 1)}{4}=\frac{3\times(30 + 1)}{4}=23.25$. Locate 23.25 on the cumulative - frequency axis and read off the distance on the x - axis, which is 34000 km.

Answer:

a. 20
b. 30000
c. 24000
d. 34000