Question

drivers pay a toll to pass over a busy bridge, and there are many toll booths that collect money. the city manager counted the total number of cars waiting to pay their tolls at 15 - minute intervals during the day for a total of 50 observations. the histogram below shows the results. which interval contains the median number of cars in line? 10 - 20 cars 20 - 30 cars 30 - 40 cars 40 - 50 cars

Explanation:

Step1: Find the median position

For \(n = 50\) observations, the median is the \(\frac{n + 1}{2}=\frac{50+1}{2}=25.5^{th}\) value (the average of the \(25^{th}\) and \(26^{th}\) values when data is ordered).

Step2: Calculate cumulative frequencies

• For the interval \(0 - 10\): frequency \(f_1=4\)
• For the interval \(10 - 20\): frequency \(f_2 = 12\), cumulative frequency \(CF_1=4 + 12=16\)
• For the interval \(20 - 30\): frequency \(f_3=18\), cumulative frequency \(CF_2=16+18 = 34\)

Since \(16<25.5<34\)

Answer:

20 - 30 cars