analyze - make a mathematical analysis of the material 

prediction - a statement about the way things will happen in the future, often but not always based on experience or knowledge

measures of central tendency - Mean, median, and mode which are used to summarize and organize a set of data

mean - sum of data items divided by the number of data items

median - the middle value in an ordered set of numbers

mode - the data item that occurs the greatest number of times in a data set 

interquartile range - the difference between the first and third quartile

outlier - a value that is much greater or much less than the rest of the data

bivariate data - data that shows the relationship between two variables or two sets of data

univariate data - data that involves a single relationship of one variable

Students will compare measures of central tendency by selecting a sport and recording this data on a worksheet with 95% accuracy.

Students will write a summary report for the collection of data to compare the two types of graphical representations and the differences and similarities between the data with 95% comprehension.

60 - 80 minutes

• recording worksheet      C:\Documents and Settings\Teacher\My Documents\Data Collection Worksheet.docx
•  Measures of Central Tendency Worksheet   C:\Documents and Settings\Teacher\My Documents\Questions for Sports Measures of Central Tendency.docx
• Mean and Median Resource from Thinkfinity to determine mean and median: http://illuminations.nctm.org/ActivityDetail.aspx?ID=160
• Laptop computer
• Paper
• Pencil
•  Individual Response devices (if available)
•  graphing calculator (if available)

W: Explain to the students that they will be completing a project that will require that they analyze data, make predictions and observations about sports data using the measures of central tendency and present this data in report format.

H: Ask introductory questions of the students to present the lesson relating to measures of central tendency and their relation to sports.

E:  Question students about the measure of central tendency.  Present the website and worksheets needed to complete the lesson to the students.  Once the students have collected the data use the Thinkfinity resource to calculate the measures of central tendency.

R:  Students will meet in groups to discuss their collected data and students will determine if these results will make sense.  Students will determine if there are any outliers in the data and the effect that these cause on the data.  Students will make a comparison of the data and consider all aspects that affect the data.  Students will prepare to report on the data.

E: Students will individually complete an essay to discuss a series of questions about measures of central tendency and the data that they have collected to make predictions about the data.

T:  The teacher will devise a mini quiz to inquire knowledge of the students' understanding of measures of central tendency.  Students needing additional assistance will be placed into small groups to receive additional assistance.  The other students will collect data on the March madness basketball tournament for the previous year and determine the measures of central tendency and any conclusions that can be drawn.

O: The focus of the lesson is to gather bivariate data about one sport and the two different gender teams that play that sport, organize and analyze this data, interpret the application of the data, and present this data in a report format.  Students will after collecting this data apply the measures of central tendency to make determinations about the teams and determine if gender has an impact on performance.

This lesson is designed for an Algebra 1 classroom from grades seventh through twelveth.  With modifications this lesson can be used in Pre-Algebra classrooms or Algebra 2 classrooms.

W: "In today's lesson, we are going to gather bivariate data, organize and analyze the data by measures of central tendency, interpret the application of the data to the real-world practical application and present the data in a report format."

H: "How do sports data relate to mathematics?" <allow time for students to respond> (Some examples are: collection of statistics for points, goals, touchdowns, first place finishes)  "Are there displays that express the statistics of basketball into measures of central tendency, scatter plots, and box - and - whiskers plots?" (yes, these can appear in sports magazines to show comparison of data) <allow time for students to respond> "What are the measures of central tendency?"  (mean, median, and mode) <allow time for students to respond> "Today, we will be looking at how a NCAA sport's data can be used to draw these type of conclusions and how these displays can allow a person to look at and compare a female team's statistics to a male team's statistics to draw conclusions as to which is the better overall team."

E:  Students will work in small groups and will have background knowledge of the material concepts to be completed.  "Remember what the measures of central tendency are?" (mean, median, and mode) <Students will provide information> "What is a mean?" (the average of the numbers in the data set) <Students will provide information> "What is a median?" (the middle number in the data set once the data set has been placed in numerical order) <Students will provide information>  "What is a mode"  (the most occurring value in the data set) <Students will provide information>  "Using the website http://www.ncaa.com/statistics/index.html, choose an NCAA team for data collection.  Collect data for both the male and female teams for that sport.  Use the data collection worksheet to record these numbers.  Also, select and indicate which category of reporting statistics will be used.  Once all the data is collected complete the "Measures of Central Tendency Worksheet. Use the Thinkfinity resource on calculating mean and median to check your calculations found at the URL http://illuminations.nctm.org/ActivityDetail.aspx?ID=160."

R: "Now, look at the collected data and with your group draw determinations as to whether this data makes sense for the particular category of data that is being used (points per game, fouls, errors).  Are there any data items that would qualify to be an outlier for either team?  If so, discuss with your group what effect this will have on the measures of central tendency. Also, discuss with your group any conclusions that can be drawn using the measures of central tendency as to how both teams compare.  Be sure to discuss all aspects that can be considered and be prepared to write an essay on the display of each team and comparsion of the two teams.  Determine whether gender has an impact on the overall performance of the team.  How can measures of central tendency be used to make predictions about sports data? How can measures of central tendency be used to make predictions about other real world applications? Give examples of these applications and where the applications would be used."

E:  Students will compare these plots as a group. Individually each student will create an essay to discuss:

• which team has the best overall record in the category selected;
• how each measure describes the data;
• describe if either team has an outlier data and the effect that this item(s) has on the overall data; 
• determine whether gender has an impact on the overall performance of the team;
• how the measures of central tendency can be used to make predictions about sports teams;
• what real world applications could be predicted using measures of central tendency and how could these be used to make predictions using the data.

T: The following strategies will be used to tailor the lesson to each student's needs:

Teacher will devise a mini quiz of questions about measures of central tendency.  Students' response will be reviewed and those students needing additional assistance on this concept will be placed into a small group to receive additional assistance.

Extension: Students will be using the data of the March madness basketball tournament for the previous year to determine the measures of central tendency for the tournament scores and to determine if there is a pattern and/or if any outliers exist in the scores. 

O: The focus of the lesson is to gather bivariate data about one sport and the two different gender teams that play that sport, organize and analyze this data, interpret the application of the data, and present this data in a report format.  Students will after collecting this data apply the measures of central tendency to make determinations about the teams and determine if gender has an impact on performance.

Students' progress will be monitored by:

• inspection of the graphs being created;
• pair-share discussion checklists completed daily;
• mini quizzes with questions being answered through the interactive use of individual response devices with questions being placed on the interactive white board;
• correct usage of vocabulary associated with this section.

• recording worksheet      C:\Documents and Settings\Teacher\My Documents\Data Collection Worksheet.docx
• Measures of Central Tendency Worksheet   C:\Documents and Settings\Teacher\My Documents\Questions for Sports Measures of Central Tendency.docx
•  Mean and Median Resource from Thinkfinity to determine mean and median: http://illuminations.nctm.org/ActivityDetail.aspx?ID=160