Question

A random sample of 40 bus riders was surveyed on a particular stop of a route on a Monday between 1:00 and 2:00 pm. The frequency distribution below shows the distribution of wait times for a bus (in minutes). Show all work for the following questions.
Wait Time (minutes) Frequency Cumulative Relative Frequency

1.0 – 2.9 7
3.0 – 4.9 14
5.0 – 6.9 0.750
7.0 – 8.9 0.900
9.0 – 10.9 1.000
Total 40

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to three decimal places.
(b) What percentage of the wait times was less than 5 minutes?
(c) Which of the following wait time groups does the median of this distribution belong to? 1.0 – 2.9, 3.0 – 4.9, 5.0 – 6.9, 7.0 – 8.9, or 9.0 – 10.9? Explain.

Answer 1

Solution:

a)

(b) What percentage of the wait times was less than 5 minutes?

Answer: 52.5%

(c) Which of the following wait time groups does the median of this distribution belong to? 1.0 – 2.9, 3.0 – 4.9, 5.0 – 6.9, 7.0 – 8.9, or 9.0 – 10.9? Explain.

Answer: 3.0 - 4.9 because median is the value which divides the data into two equal halves and in the given cumulative frequency distribution, we see 52.5% of data lies in this interval and below. So the median has to be in this interval.