Question

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.
20
b. use the cumulative frequency curve to find the median distance. 12800
c. use the cumulative frequency curve to find the lower quartile. type your answer...
d. use the cumulative frequency curve to find the upper quartile. type your answer...
e. hence write down the interquartile range. type your answer...
f. find the number of buses that travelled a distance less than or equal to 5500 km.

Explanation:

Step1: Understand cumulative - frequency concept

The cumulative - frequency at a certain value gives the number of data points less than or equal to that value.

Step2: Find lower quartile

The lower quartile ($Q_1$) is the value at the 25th percentile. If the total number of data points (from the maximum cumulative - frequency) is $n$, we find the value on the cumulative - frequency curve corresponding to $\frac{n}{4}$. Looking at the curve, if we assume the total number of buses (maximum cumulative - frequency) is 120, then $\frac{120}{4}=30$. Reading from the curve, the lower quartile is approximately 8000.

Step3: Find upper quartile

The upper quartile ($Q_3$) is the value at the 75th percentile. For $n = 120$, we consider $\frac{3n}{4}=90$. Reading from the curve, the upper quartile is approximately 18000.

Step4: Calculate inter - quartile range

The inter - quartile range (IQR) is $Q_3 - Q_1$. So, $IQR=18000 - 8000=10000$.

Step5: Find number of buses for 5500 km

We read the cumulative - frequency value corresponding to 5500 km on the curve. It is approximately 10.

Answer:

c. 8000
d. 18000
e. 10000
f. 10