Activities

1. What can be said about the mean absolute deviation in the graphs below?

2. Two social studies classes took the same test that was scored out of 100 points.  Mr. Map says his class had a median score of 78 and a range of 4 points, while Ms. Glee claims that her class had a median score of 78 and a range of 22 points. Is it possible that these classes could have the same median score while having very different ranges?

3. Olivia has 6 test scores in her science class so far this year. She determines that her median score of these six scores is 88. During the next month, she gets a 92, her best score so far, and a 68, her lowest score so far. What is the median score of all eight scores? Explain your answer.

4. A survey-taker randomly selected 50 people as they were leaving a museum and asked how much time they had spent in the museum. The mean response was 70 minutes. She randomly selected 300 people leaving the museum the next week and asked the same question. The mean response for this group was 100 minutes.
   
   What might explain this difference in responses?

5. Find out which set of data has less variability based on the mean absolute deviation. Show your work.

6. The median of Data Set A equals the median of Data Set B. Each set consists of exactly five numbers. Give an example of two sets of data that match the description.

Answer Key/Rubric

1. Graph 2 would have a higher MAD than graph 1.

2. Yes they could have the same median score.  The median is the value in the middle and they could have the same middle number even with different ranges.

3. Olivia has a median score of 88 after she gets her two new test scores.  Reason why might include but are not limited to,

• The new test scores cancel each other out when finding the mean because one is higher than the mean and one is lower than the mean.
• The mean stays the same because the new tests scores are on opposite ends of the list of scores if they were put in numerical order.

4.  Reasons for different responses might include, but are not limited to,

• The second survey had more people taking it
• Maybe the museum was busier on the second day so it took longer to see all the displays
• The exhibits might have been different in the museum each week

5. The second set of data has less variability based on the MAD.  Student work might include but is not limited to,
   
   First set of data has a MAD of 8

The MAD of the second set of data is 4.

The second set of data has less variability based of the MAD. 

6. Answer will vary, student work might include but is not limited to,

• Student could set up a table and have the median numbers be the same value.  All the other numbers in the table could be placed without changing the median.  Each set of data needs two values greater than 25 and two values less than 25 in this example.