Question

using the histograms, which of the following is the correct comparison of the distributions?the 10 - 20 interval contains the most observations on both days.the two distributions for number of cars in line are both skewed right.the median number of cars for both distributions lies in the 20 - 30 interval.there were more than 40 cars in line more often on the weekend than the weekday.

Explanation:

Step1: Analyze each option

• Option 1:
• In the first histogram (weekday), the interval with the most observations is \(20 - 30\) (not \(10 - 20\)).
• Option 2:
• A right - skewed distribution has a longer tail on the right. In the first histogram (weekday), the tail is on the right. In the second histogram (weekend), the tail is also on the right.
• Option 3:
• For the first histogram (weekday), if we assume the total number of observations \(n_1=4 + 13+17 + 8+5+1=48\). The median is the \(\frac{n_1 + 1}{2}=24.5^{th}\) observation. Cumulative frequencies: \(0 - 10:4\), \(10 - 20:4 + 13 = 17\), \(20 - 30:17+17 = 34\). The median lies in \(20 - 30\).
• For the second histogram (weekend), assume the total number of observations \(n_2=12+17+14+3+1 = 47\). The median is the \(\frac{n_2+1}{2}=24^{th}\) observation. Cumulative frequencies: \(0 - 10:12\), \(10 - 20:12 + 17=29\). The median lies in \(10 - 20\) (not \(20 - 30\)).
• Option 4:
• For the first histogram (weekday), the number of observations with more than \(40\) cars is \(5 + 1=6\). For the second histogram (weekend), the number of observations with more than \(40\) cars is \(3+1 = 4\). So, there were not more than \(40\) cars in line more often on the weekend than the weekday.

Answer:

The two distributions for number of cars in line are both skewed right.