Worksheet

Robot Trials: Precision and Consistency

Analyze robot test results using mean, median, IQR, and MAD, then interpret consistency, distribution patterns, and an outlier.

Grade 6MathInteractive · Printable

Aligned to6.SP.B.5.c

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Single worksheet
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1 Common Core standard
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13 questions
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Details

Format: Interactive · Printable
Grade: Grade 6
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students calculate mean, median, interquartile range, and mean absolute deviation from robot test data.
Students describe distribution patterns and identify a striking outlier.
Students use measures of center and spread to evaluate robot performance.

How to use

Have students work through the three testing stages. For odd-sized data sets, exclude the median when finding quartiles. Discuss the final evidence statements as a class.

Curriculum

Common Core standard covered

6.SP.B.5.c

Find the median, mean, interquartile range, and mean absolute deviation, and describe the pattern and any striking outliers.

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Robot Trials: Precision and Consistency

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.

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

Use the completed stopping-distance record. Which statement correctly identifies its median?

A. The median is 21 cm, the average of all five results.
B. The median is 22 cm, the middle of the four different results.
C. The median is 20 cm, the third result in the sorted record.
D. The median is 21.5 cm, halfway between the two endpoints.

For the completed stopping-distance record, find the spread of the middle half of the results.

IQR = cm

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.

Which pair correctly summarizes the center of the course times?

A. The mean is 9 seconds, and the median is 8 seconds.
B. The mean is 8 seconds, and the median is 9 seconds.
C. The mean is 9 seconds, and the median is 9 seconds.
D. The mean is 8 seconds, and the median is 8 seconds.

The course times have a MAD of 2 seconds. What does this tell the club?

A. The middle half of the course times spans 2 seconds.
B. The course times are, on average, 2 seconds from their mean.
C. The course times increase by 2 seconds after each trial.
D. The longest and shortest course times differ by 2 seconds.

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

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?

A. Do not approve it because its MAD exceeds the allowed limit.
B. Approve it because its MAD is less than its mean.
C. Approve it because meeting the mean requirement is enough.
D. Do not approve it because its mean exceeds the allowed limit.

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?

A. The times cluster from 6 to 9 seconds, with an isolated high outlier.
B. The times form two equal-sized clusters separated by a gap.
C. The times are evenly spread, with no clear cluster or outlier.
D. The times are symmetric, with most results near 14 seconds.

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.

The 32-second result makes the mean greater than the median.The 32-second result proves that the timer was broken.Six of the seven pickup times fall between 6 and 9 seconds.The histogram shows that pickup times increased in trial order.The unusual trial deserves investigation, but these times do not reveal its cause.