Question

two airlines have data on the arrival times of their flights. an arrival time of +2 minutes means the flight arrived 2 minutes early. an arrival time of -4 minutes means the flight arrived 4 minutes late. skyhigh airlines has a mean arrival time of 1.5 minutes with a standard deviation of 10.6 minutes. skyview airlines has a mean arrival time of -4 minutes with a standard deviation of 5 minutes. explain the meaning of these figures and why they would affect your choice of airline.

choose the correct answer below.

a. if you want to avoid common delays, skyview airlines might be the better choice. skyview airlines on average runs slightly ahead of schedule, and it tends to have smaller delays. while skyhigh airlines on average runs slightly behind of schedule, it can also have long delays (late arrivals).
b. skyview airlines is always the better choice because it tends to have smaller delays.
c. if you want to avoid long delays, skyview airlines might be the better choice. skyview airlines on average runs slightly behind schedule, but it tends to have smaller delays. while skyhigh airlines on average runs ahead of schedule, it can also have long delays (late arrivals).
d. skyhigh airlines is always the better choice because, on average, it runs ahead of schedule.

Explanation:

Interpret the mean arrival times

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

• SkyHigh Airlines: Mean arrival time is \(+1.5\) minutes. Since positive values represent early arrivals, SkyHigh runs on average \(1.5\) minutes early (ahead of schedule).
• Skyview Airlines: Mean arrival time is \(-4\) minutes. Since negative values represent late arrivals, Skyview runs on average \(4\) minutes late (behind schedule).

Interpret the standard deviations

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

• SkyHigh Airlines: Standard deviation is \(10.6\) minutes. This larger spread indicates higher variability, meaning it is more prone to extreme values, such as long delays.
• Skyview Airlines: Standard deviation is \(5\) minutes. This smaller spread indicates more consistent arrival times with smaller deviations from its mean.

Evaluate the decision choices

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

• If you want to avoid long delays, Skyview Airlines is the better choice because its smaller standard deviation (\(5\) minutes vs. \(10.6\) minutes) means its arrival times are much more consistent and less spread out, making extreme long delays less likely.
• This is true even though Skyview on average runs slightly behind schedule (mean of \(-4\) minutes) compared to SkyHigh, which on average runs ahead of schedule (mean of \(+1.5\) minutes) but has a much higher risk of long delays due to its high variability.
• This matches option C.

Answer:

• (A) If you want to avoid common delays, Skyview Airlines might be the better choice. Skyview Airlines on average runs slightly ahead of schedule, and it tends to have smaller delays. While SkyHigh Airlines on average runs slightly behind schedule, it can also have long delays (late arrivals).
• (B) Skyview Airlines is always the better choice because it tends to have smaller delays.
• (C) If you want to avoid long delays, Skyview Airlines might be the better choice. Skyview Airlines on average runs slightly behind schedule, but it tends to have smaller delays. While SkyHigh Airlines on average runs ahead of schedule, it can also have long delays (late arrivals). (Correct answer)
• (D) SkyHigh Airlines is always the better choice because, on average, it runs ahead of schedule.