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.

A histogram titled Bridge Toll Booth Traffic has number of cars in line on the x-axis and frequency on the y-axis. 0 to 10, 4; 10 to 20, 13; 20 to 30, 18; 30 to 40, 8; 40 to 50, 5; 50 to 60, 1.

Which interval contains the median number of cars in line?

10–20 cars
20–30 cars
30–40 cars
40–50 cars

To determine the interval containing the median number of cars in line, we first need to identify the median's position in the dataset. The median is the middle value when the data is ordered, so for 50 observations, the median will be the average of the 25th and 26th values.

Here's how we find it:

1. **Intervals and Frequencies:**
   - 0 to 10 cars: 4 observations
   - 10 to 20 cars: 13 observations
   - 20 to 30 cars: 18 observations
   - 30 to 40 cars: 8 observations
   - 40 to 50 cars: 5 observations
   - 50 to 60 cars: 1 observation

2. **Cumulative Frequency:**
   - 0 to 10 cars: 4 (cumulative frequency = 4)
   - 10 to 20 cars: 13 (cumulative frequency = 17)
   - 20 to 30 cars: 18 (cumulative frequency = 35)
   - 30 to 40 cars: 8 (cumulative frequency = 43)
   - 40 to 50 cars: 5 (cumulative frequency = 48)
   - 50 to 60 cars: 1 (cumulative frequency = 49)

3. **Finding the 25th and 26th Observations:**
   - The 25th and 26th observations fall in the cumulative frequency range of 18 to 35, which corresponds to the **20 to 30 cars** interval.

Thus, the median number of cars in line falls within the **20–30 cars** interval.

Would you like more details or have any questions? 

Here are 5 related questions to consider:
1. How is the median different from the mean in a dataset?
2. Why is it important to know the median in traffic management?
3. How would you calculate the mean number of cars in line from the given data?
4. What might the shape of the distribution suggest about traffic patterns on this bridge?
5. How could outliers affect the interpretation of this data?

**Tip:** When working with histograms, always pay attention to cumulative frequencies for pinpointing medians.

Discover which interval contains the median number of cars in line at a bridge toll booth using statistical analysis. This problem involves interpreting a histogram of car counts over time intervals and calculating the median from frequency data. Suitable for high school students studying statistics and data analysis.

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