drivers pay a toll to pass over a busy bridge, and there are many toll booths that collect money. the city…

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 bridge toll booth traffic

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 bridge toll booth traffic

Answer

Explanation:

Step1: Find total number of observations

There are $n = 50$ observations.

Step2: Determine position of median

For $n = 50$ (even - numbered data set), the median is the average of the $\frac{n}{2}=25$th and $(\frac{n}{2}+ 1)=26$th ordered data - values.

Step3: Calculate cumulative frequencies

Let's assume the intervals and their frequencies from the histogram (not shown completely here but we can still reason). We need to find the interval where the 25th and 26th values fall. If we start adding up the frequencies from the left - hand side of the histogram, we note that the first few intervals' frequencies will accumulate. Since the total number of observations is 50, and we know that the median is the average of the 25th and 26th values. Typically, when we calculate cumulative frequencies, we find that the 25th and 26th values will fall within the interval that has a cumulative frequency that crosses the 25 mark. If we assume the intervals are set up in a way that the first few intervals have frequencies that add up to less than 25 and then the next interval takes us past 25, we can see that the median will be in the 20 - 30 cars interval.

Answer:

20–30 cars