Launch Day: Choose a Useful Summary

Use data shape and purpose to choose measures of center and variation.

Flight Altitudes

Choose summaries that fit the data. MAD means mean absolute deviation; IQR means interquartile range.

A model rocket team measures the highest altitude reached in 21 launches using the same motor type. Each histogram interval includes its lower endpoint but not its upper endpoint.

Which description best fits the altitude distribution?

A. It has two widely separated clusters of altitudes.B. It has a long tail toward higher altitudes.C. It has equal counts in every altitude interval.D. It is roughly symmetric around its middle interval.

The team wants a center and a measure of typical distance from that center. Which pair is well suited to this roughly symmetric distribution?

A. Use the mean and maximum.B. Use the range and IQR.C. Use the mean and MAD.D. Use the median and mean.

Why is the mean a reasonable center for these altitudes?

A. The balanced shape has no isolated extreme interval.B. The mean must equal the tallest altitude recorded.C. The tallest bar makes variation unnecessary to report.D. The mean ignores launches in the outer intervals.

Two motor types produce roughly symmetric altitude distributions without unusual values. Both have a mean altitude of 85 m. The first has a MAD of 4 m; the second has a MAD of 9 m.

For more consistent altitudes, choose the motor type with a MAD of m.

Recovery Times

Use the recovery records to decide which summaries describe a typical launch without being strongly affected by an unusually long recovery.

Recovery time runs from landing until a team member returns the rocket to the launch desk. The sorted times for nine launches were 3, 4, 4, 5, 5, 6, 6, 7, and 23 minutes. The 23-minute recovery involved a rocket caught in a tree.

Which pair best summarizes the typical recovery time and the spread of the middle half of these times?

A. Use the mean and range.B. Use the maximum and MAD.C. Use the mean and minimum.D. Use the median and IQR.

What is the median recovery time? minutes

For this box plot, Q1 = 4 minutes and Q3 = 6.5 minutes.

What is the IQR? minutes

Select the two statements that explain why the median and IQR fit the team's goal.

Suppose the tree recovery had taken 41 minutes instead of 23 minutes, with all other times unchanged. Which statement would be true?

A. The median and IQR would both increase.B. The median and IQR would both stay unchanged.C. The mean and range would both stay unchanged.D. The mean would decrease and the range would increase.

Match the Summary to the Decision

For each new launch-day decision, consider the purpose as well as the shape of the data.

10.

Priya plans battery use for tracking devices. Battery use per flight is right-skewed because a few flights require much longer tracking. She wants to estimate total battery use for 30 similar flights by multiplying one measure of center by 30. Which choice fits that purpose?

A. Use the mean because it includes the use from long tracking sessions.B. Use the median because it excludes the effect of long tracking sessions.C. Use the IQR because it describes the middle half of battery use.D. Use the minimum because it describes the least battery use possible.

11.

A launch organizer compares waiting times at two check-in desks. Both distributions have long right tails. She wants to compare the variability of the middle half of the waits without letting the longest waits dominate. Which measure fits?

A. The maximum fits because it gives the longest wait.B. The IQR fits because it measures the middle-half spread.C. The mean fits because it adds all the waiting times.D. The range fits because it uses the two extreme waits.

12.

Two parachute designs have roughly symmetric flight-duration distributions with no unusual values. The team wants flights near 40 seconds with little variation. Use the summaries to choose a design.

Parachute trials
Design	Mean (seconds)	MAD (seconds)
Ribbon	40	7
Round	40	3

A. Choose Round: its smaller MAD means its mean flight duration is lower.B. Choose Ribbon: its larger MAD means all flights are closer to 40 seconds.C. Choose Round: the same mean comes with a smaller typical distance from it.D. Choose Ribbon: the same mean comes with less variation in flight duration.

13.

A launch-day report lists these two groups of setup times: Quick-release stands: 2, 2, 3, 3, 4, 4 minutes. Screw-lock stands: 2, 2, 3, 3, 4, 16 minutes. Noah says, “The means are always the fairest way to compare typical setup times because they use every value.” Explain why his rule is too broad. Recommend a center and a matching measure of variation for each group, using the data as evidence.