Lesson 5: Describing a Distribution Displayed in a Histogram

Brazil, 2014

I am successful when I can:1.) Calculate relative frequency

2.) Make a relative frequency histogram

3.) Compare a relativefrequency histogram and a frequency histogram to decide which best represents data

Please Turn Back to your Success Criteria Paper and Complete the Table and Questions

Comparing Frequency Table and Relative Frequency Table

1.) Describe the shape of the relative frequency histogram of Appearances in the World Cup. 2.) How does the shape of this histogram compare with the frequency histogram done at the beginning of the class? 3.) What could be some reasons why so many teams have few appearances? 4.) In what situations would it be better to use a regular frequency table with tally only or a relative frequency table?

Converting Fractions Decimals Percent

Questions: 1.) Which letter grade has the greatest relative frequency? What is the value? 2.) What letter grades have the highest and lowest relative frequencies? What is the difference in their relative frequencies? Please show work. 3.) What percent of students scored above a D? Please show work. 4.) Would you consider this data set categorical or numerical. Please explain your reasoning.

Please take out your grade 6 books and turn to Lesson 5: page S.28

and complete exercises 1-4

SOUTHAFRICA 2010 Number of Goals Scored: Table of Relative Frequency

16 1 16 #16/145 0.11 11%15 0 0 0 0 014 0 0 0 0 013 0 0 0 0 012 1 12 #12/145 0.08 8%11 1 11 #11/145 0.08 8%10 1 10 #10/145 0.06 6%9 1 9 #9/145 0.06 6%8 1 8 #8/145 0.06 6%7 1 7 #7/145 0.05 5%6 1 6 #6/145 0.04 4%5 3 15 #15/145 0.1 10%4 4 16 #16/145 0.11 11%3 8 24 #24/145 0.17 17%2 4 8 #8/145 0.05 5%1 3 3 #3/145 0.02 2%

TOTAL 145 #145/145 0.99 99%

Questions (answered with your groups):

Look at the table ‘Number of Goals Scored’ in the World Cup in Southafrica 2010. 1.) What is the maximum number of net goals scored and how many teams scored this number of goals? 2.) What was the typical number of goals scored? Express this number as a relative frequency. 3.) If you were to make a relative frequency graph, what data would be on the horizontal axis and what data would be on the vertical axis? What would be your bin size?

BRAZIL 2014

Number of Goals Scored (06/23/2014)Table of Relative Frequency

Net Goals Goals per Team Frequency Relative Frequency Relative Frequency Percent7 1 7 7/115 0.06 6%6 2 12 12/115 0.1 10%5 2 10 10/115 0.09 9%4 7 28 28/115 0.24 24%3 11 33 33/115 0.29 29%2 5 10 10/115 0.09 9%1 15 15 15/115 0.13 13%

TOTAL 115 115/115 1.00 100%

4.) Looking at the Frequency Histograms, what similarities and differences do you observe? What do you notice about the shapes?

4.) Looking at the Frequency Histograms, what similarities and differences do you observe? What do you notice about the shapes?

5.) Using both tables, list and then compare the frequencies and relative frequencies of scoring 4 net goals. Why is there a greater difference in relative frequency than in frequency?

6.) In what situations would it be preferable to use a histogram? In what situations would it be preferable to use a frequency histogram?

Extension Questions:

1.) What is the percent of category 1-3 goals in 2010? In 2014? Why do you observe the difference?

2.) Why is the percent for the 7-9 goals so low for the 2014 world cup as compared to 2010?

3.) The media has said that the 2014 is the “World Cup of the Goals”. Using the information you were given, do you agree

or disagree?

4.) Using the information you have, make an informed prediction of the total number of goals scored.

Extending the Math (Homework Ideas) Mathematics Across Content Areas:

- Website for the FIFA 2014 World Cuphttp://www.fifa.com/

-Website for the FIFA 2010 World Cup (and all other editions since Uruguay 1930)

http://www.fifa.com/tournaments/archive/worldcup/southafrica2010/statistics/matches/goals.html

-Links to articles of interest for middle and high school studentshttp://www.nytimes.com/sports/worldcup/

http://www.espnfc.us/

http://www.espnfc.us/fifa-world-cup/story/1907511/united-states-portugal-world-cup-match-draws-record-television-ratings

Practice Standards Implemented: MP. 2Reason Abstractly and QuantitativelyStudents use graphs to summarize the data and answer statistical questions.

MP.6Attend to PrecisionStudents interpret and communicate conclusions in context based on graphical and numerical data summaries.