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 relative
frequency 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
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
TOTAL
1
0
0
0
1
1
1
1
1
1
1
3
4
8
4
3
16
0
0
0
12
11
10
9
8
7
6
15
16
24
8
3
145
#16/145
0
0
0
#12/145
#11/145
#10/145
#9/145
#8/145
#7/145
#6/145
#15/145
#16/145
#24/145
#8/145
#3/145
#145/145
0.11
0
0
0
0.08
0.08
0.06
0.06
0.06
0.05
0.04
0.1
0.11
0.17
0.05
0.02
0.99
11%
0
0
0
8%
8%
6%
6%
6%
5%
4%
10%
11%
17%
5%
2%
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 Percent
7
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?
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 Cup
http://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 students
http://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-recordtelevision-ratings
Practice Standards Implemented:
MP. 2
Reason Abstractly and Quantitatively
Students use graphs to summarize the data and
answer statistical questions.
MP.6
Attend to Precision
Students interpret and communicate conclusions in
context based on graphical and numerical data
summaries.