Kathryn White - Missouri S&T



Kathryn White

Making Sense of Data

High School

Summer 2003

Topics: Presentation of Data

Box Plot

Line Plot

Back-To-Back Stem & Leaf Plot

Objectives:

Students will create, interpret and compare different data displays.

Students will choose an appropriate data display.

Missouri State Standards:

MA-3: 1.6, 1.8, 2.1, 3.4, 4.1

Pre-requisite Skills:

Students can create box plots, line plots and back-to-back

stem & leaf plots.

Materials/Handouts:

Challenger Space Shuttle Launch Temperature vs. Success Data

Challenger Space Shuttle Story

Challenger Space Shuttle Activity Worksheet

Graph paper

Overhead Projector & Blank Overhead sheet

Procedure:

A) Divide students into groups of 3 at most.

B) Read the Challenger Space Shuttle Story or provide each group with a copy of the story to read individually.

C) Present the Challenger Space Shuttle Launch Temperature vs. Success Data to the class either on the overhead or as a handout. Create the scatter plot on the overhead of the data that was looked at during the teleconference (only the data of the failures is plotted). Note the U-configuration mentioned in the story. Discuss that any O-ring damage is considered a Failure and no O-ring damage is considered a success and that when the data was originally considered they only looked at temperatures where the O-rings had failed.

D) Give each group one Challenger Space Shuttle Activity Worksheet. Try to make sure that the 3 different versions of the activity sheets are given out. Allow students time to work on the activity sheet. At least one group should create a box plot display with one box plot for successes and one box plot for failures. At least one group should create a line plot for success (S) and failures (F). At least one group should create a back-to-back stem and leaf plot for successes and failures.

D) Have the groups present their formal argument which should be based on their data display.

E) To conclude, present all 3 types of data displays (I have students lay an overhead sheet over their graph paper and copy their display) simultaneously and discuss the differences in data presentation and which display most clearly shows the effect of temperature. Be sure to note that the data displays show all of the available data. You may want to present the scatter plot again.

Assessment:

Ask students to write a paragraph explaining what mistake the Rogers Commission had found in the analysis of the historical data.

Extensions:

• Use a graphing calculator to display the data.

• Explore what decisions may have been made if only the success data had been displayed.

References:

James M. Landwehr, Ann E. Watkins. Exploring Data. Dale Seymour Publications, 1999, pp 144-145.

Challenger Space Shuttle Activity

Worksheet

Do Not Write On This Worksheet

TASK I

Create a Box Plot of the Shuttle Launch data.

TASK II

Provide your group’s analysis in writing as to whether the Space Shuttle should be launched. You must include your graphic display and use it to support your decision.

TASK III

Present your analysis to the class.

TASK IV

Each group member must write a unique paragraph about what they learned from this experience about using data, different graphic displays and what their role was in the group.

Challenger Space Shuttle Activity

Worksheet

Do Not Write On This Worksheet

TASK I

Create a Back-To-Back Stem & leaf Plot of the Shuttle Launch data.

TASK II

Provide your group’s analysis in writing as to whether the Space Shuttle should be launched. You must include your graphic display and use it to support your decision.

TASK III

Present your analysis to the class.

TASK IV

Each group member must write a unique paragraph about what they learned from this experience about using data, different graphic displays and what their role was in the group.

Challenger Space Shuttle Activity

Worksheet

Do Not Write On This Worksheet

TASK I

Create a Line Plot of the Shuttle Launch data.

TASK II

Provide your group’s analysis in writing as to whether the Space Shuttle should be launched. You must include your graphic display and use it to support your decision.

TASK III

Present your analysis to the class.

TASK IV Each group member must write a unique paragraph about what they learned from this experience about using data, different graphic displays and what their role was in the group.

Challenger Space Shuttle

Launch Temperature vs. Success Data Sheet

|Date |Temperature |# Damaged O-rings |

|4/21/81 |66 |0 |

|11/12/81 |70 |1 |

|3/22/82 |69 |0 |

|6/27/82 |80 |Data not available |

|1/11/82 |68 |0 |

|4/4/83 |67 |0 |

|6/18/83 |72 |0 |

|/8/30/83 |73 |0 |

|11/2/83 |70 |0 |

|2/3/84 |57 |1 |

|4/6/84 |63 |1 |

|8/30/84 |0 |1 |

|10/5/84 |78 |0 |

|11/8/84 |67 |0 |

|1/24/85 |53 |3 |

|4/12/85 |67 |0 |

|4/29/85 |75 |0 |

|6/17/85 |70 |0 |

|7/29/85 |81 |0 |

|8/27/85 |76 |0 |

|10/3/85 |79 |0 |

|10/30/85 |75 |2 |

|11/26/85 |76 |0 |

|1/12/86 |58 |1 |

|1/28 |31 |Challenger Accident |

Challenger Space Shuttle Story

On January 28, 1986, the Challenger space shuttle was launched from the Kennedy Space Center in Florida. Shortly into the flight it exploded, killing all seven crew members. After the accident, President Reagan appointed a commission headed by former Secretary of State William Rogers to find the cause. The Rogers Commission report included the following information:

The night before the launch there was a three-hour teleconference among people from the Kennedy Space Center, NASA (National Aeronautics and Space Administration), and the company that manufactured the solid rocket motors. The discussion focused on the predicted 31 degree Fahrenheit temperature at launch time and the possible effect of such a low temperature on O-ring performance. The O-rings seal the joints between different sections of the solid rocket motors. In essence, each O-ring is a large rubber washer about 35 feet in diameter and ¼ inch thick. After a shuttle is successfully launched, the rocket motors are jettisoned into the ocean and recovered. The O-rings can then be examined for possible damage that occurred during the launch. Thus, data were available from 23 previous space shuttle launches giving the temperature at launch time and the number of incidents of O-ring damage in that launch.

During the teleconference the night before the Challenger launch, a data set and associated scatter plot played an important role in the discussion. Each plotted point represents one of the seven shuttle flights that experienced some O-ring damage; the horizontal axis shows the temperature at launch and the vertical axis shows the number of O-rings that sustained damage in these flights.

The teleconference participants debated whether these historical data implied a temperature effect on O-ring performance. Some participants recommended that the launch be postponed until the temperature rose above 53 degrees Fahrenheit – the lowest previous launch temperature – because that flight had the largest number of damaged O-rings. Some participants also stated that separate physical evidence suggested a temperature effect on O-ring performance. On the other hand, the history showed that the second largest number of damaged O-rings occurred at the highest temperature. Ultimately, based on the U configuration of points in the scatter plot, it was concluded that there was no evidence from the historical data about a temperature effect. The official recommendation from the rocket manufacturer to NASA stated that the temperature data were not conclusive in predicting O-ring damage.

The Rogers Commission concluded that the cause of the accident was the complete failure of an O-ring on a rocket motor, which lead to the explosion. This is the type of failure that was debated the night before in the teleconference, where the participants tried to decide whether the chance of extensive O-ring damage might be substantially increased by low temperature. The temperature at launch was 31 degrees Fahrenheit. The Rogers Commission also noted that a mistake had been made in the analysis of the historical data.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download