Use center, spread, and unusual results to evaluate a school club’s robot.
1. Check the Brakes
The school robotics club measures how far its robot travels after a stop signal. Find quartiles by taking the median of each half; exclude the overall median when there is an odd number of values. MAD means mean absolute deviation.
1.
The club’s five stopping distances have a mean of 21 cm. One result is missing from the sorted record.
Stopping Distances
Trial
Distance (cm)
1
18
2
20
3
?
4
22
5
25
What distance belongs in the missing cell? cm
2.
Use the completed stopping-distance record. Which statement correctly identifies its median?
3.
For the completed stopping-distance record, find the spread of the middle half of the results.
IQR = cm
4.
Calculate the MAD of the five stopping distances. Use their mean of 21 cm.
MAD = cm
2. Test the Obstacle Course
Use the six course times and their box plot. Times are measured in seconds.
The robot completes the same course six times. Its sorted times are 4, 6, 8, 8, 10, and 12 seconds.
5.
Which pair correctly summarizes the center of the course times?
6.
The course times have a MAD of 2 seconds. What does this tell the club?
7.
The club tests a slow-motion setting. Suppose every course time becomes exactly twice its original value. Find the median and IQR of the new times.
New median = seconds; new IQR = seconds
8.
To approve the original setting, the club requires a mean course time of at most 9 seconds AND a MAD of at most 1.5 seconds. The original mean is 8 seconds and the MAD is 2 seconds. Which decision follows both requirements?
9.
Amira says, “A MAD of 2 seconds means every original course time is exactly 2 seconds away from the mean of 8 seconds.” Explain why this is incorrect. Use at least two course times as evidence.
3. Investigate a Gripper Delay
The club times how long the robot’s gripper takes to pick up a block. Analyze all seven results, including the unusually long trial.
The sorted pickup times are 6, 7, 7, 8, 8, 9, and 32 seconds. In the histogram, each interval includes its left endpoint but not its right endpoint.
10.
Which description best matches the pickup-time distribution?
11.
Calculate both measures of center for all seven pickup times.
Mean = seconds; median = seconds
12.
Find the MAD of all seven pickup times. Keep the 32-second result in the calculation.
MAD = seconds
13.
The club is writing an investigation note. Select all statements supported by the pickup-time data alone.