The Radix Endeavor - Statistics

ST1.5: Sibling Rivalry

yanchi — Fri, 01 Aug 2014 17:46:28 +0000

Quest Line:

Previous Quest:

ST1.4.2: Truth and Consequences: Part II

Summary:

Help resolve a dispute between Caldera and Felsic about how to make their pest nets keep shriekers out. They need help figuring out a good size to make the holes in the net based on the average size of the shriekers.

Recommendations:

This quest asks players to determine the difference between mode and median, the different information that they provide and which measure should be used in different cases. It asks players to think about how using the same data set can lead to different conclusions.

Learning Objectives:

Players will be able to understand the difference between median and mode and when to use each measure

Connecting Questions:

1. Discuss the three measures of central tendency that the players have used during the statistics quest lines (mean, median, mode)

2. When would you want to use the different measures (outliers, frequency)?

3. Are there cases where using the wrong measure could lead to a misleading conclusion? (if you want an average size, but use the mode, etc)

4. **The quest line does not talk about standard deviation. It could be brough up in discussion here about outliers and how this can affect using mean vs. median.

Additional Resources:

ST1.4.2: Truth and Consequences: Part II

yanchi — Fri, 01 Aug 2014 17:45:59 +0000

Quest Line:

Data Detective

Previous Quest:

ST1.4.1: Truth and Consequences: Part I

Next Quest:

ST1.5: Sibling Rivalry

Summary:

Investigating the deceptive results of the government's blackburn study, you elect to measure 6 more blackburns each in the city and volcanic desert to test your new hypothesis. (variations)

Recommendations:

In this quest players directly compare samples from two different locations and to see how data sampling can directly affect a conclusion.

Learning Objectives:

• Players will be able to create data summaries (particularly sorting by source)

• Players will be able to draw conclusions from data summaries

Tools:

Data Explorer

Data Library

Connecting Questions:

1. Were the blackburns in from both regions different in size?

2. What would have helped the government report to be more accurate?

3. Can you think of examples where collecting data only in one place might bias results? (extreme example – someone sampling the color of bears in the arctic would say that all bears are white)

4. Look through examples of reports in local news to see if it is common to disclose how data was collected for a study. Have students pick out examples where more detail might be needed.

Additional Resources:

ST1.4.1: Truth and Consequences: Part I

yanchi — Fri, 01 Aug 2014 17:45:37 +0000

Quest Line:

Data Detective

Previous Quest:

ST1.3: Crowdsourced!

Next Quest:

ST1.4.2: Truth and Consequences: Part II

Summary:

Now that you've disproven the government's blackburn study, it's time to uncover their deceptive methods. Make a hypothesis about the actual blackburn size and design a study to prove or disprove it.

Recommendations:

This quest continues to look at sample bias and good data sampling practices. The quest is asks the player to think about why the government sample might have been biased. The quest concludes when the player has decided what action to take next.

Learning Objectives:

Players will be able to draw conclusions about sampling by reading a data summary

Connecting Questions:

Wait until students have completed 1.4.1 and 1.4.2 before asking any connecting questions

Additional Resources:

ST1.1: Spines vs. Shells

yanchi — Fri, 01 Aug 2014 17:44:11 +0000

Quest Line:

Data Detective

Next Quest:

ST1.2: The Ashberry Anomaly

Summary:

Talk to Pali in Craterthwaite. Help him determine whether the lavaspines he plans on catching will fit into the crates made for average grabbleshells.

Recommendations:

This quest introduces very basic concepts in statistics – collecting a set of data in order to determine an average. It also asks player to compare two data sets by looking at the averages of each in order to make a conclusion – on average, which species is taller?. Players are given a minimum sample size that they need in order to calculate the mean.

The second part of the quest asks the player to answer specific questions about what an average represents (are all animals the same height as the average? What use is calculating a mean?)

*The Data Explorer tool in the game does the calculations for the player. The emphasis of the quest is not on the math behind the calculation of the mean, but rather on how to use statistical information to make decisions.

*The text in the quest uses the word average – players need to submit a data summary with the MEAN, not the MEDIAN

Learning Objectives:

· Players will collect data and create a data summary

· Players will be able to use a mean to compare data sets

· Players will understand how a mean is useful

Tools:

Connecting Questions:

1. Why was it useful to calculate the mean heights of both species?

2. Why can the mean be a good measure of a population?

3. This quest does not discuss standard deviation – it could be brought up at this point as an extension

Additional Resources:

Data Detective

yanchi — Fri, 01 Aug 2014 17:40:23 +0000

Investigate Antiokos's most recent claims about grabbleshells, blackburns, and other species from around Ysola. Find out how his sweeping generalizations might negatively affect the people of the island and help them determine whether the studies are accurate or not. Using concepts like mean, median, mode, and sample size, collect data and analyze it to prove who is lying with data and what should be done about it.

Standards Covered in Quest line:

• CCSSM Practice #3: Construct viable arguments and critique the reasoning of others
• CCSSM Practice #4: Use appropriate tools strategically
• CCSSM Practice #7: Look for and make use of structure
• CCSSM Statistics Standard S-ID 2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (standard deviation) of two or more different data sets
• CCSSM Statistics Standard S-IC 1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population
• CCSSM Statistics Standard S-IC, 3: Make inferences and justify conclusions from sample

Topic:

Statistics

Walkthrough:

Quests:

ST1.1: Spines vs. Shells

ST1.2: The Ashberry Anomaly

ST1.3: Crowdsourced!

ST1.4.1: Truth and Consequences: Part I

ST1.4.2: Truth and Consequences: Part II

ST1.5: Sibling Rivalry