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# Ungrouped Data to Find the Mean

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# Ungrouped Data to Find the Mean - Answer Key

## Trends in Birth Months of Soccer Players

### Topic

Trends in Birth Months of Soccer Players

### Vocabulary

• Mean
• Ungrouped Data
• Frequency Distribution Table
• Mode
• Median
• Range
• Measure of central tendency
• Bar graph

### Student Exploration

#### Are there trends in the birth months of professional soccer players?

A soccer ball.

Choose a soccer team from the European Premier Soccer League (the highest level of professional soccer in Europe), http://uk.eurosport.yahoo.com/football/premier-league/teams.html . A couple of the more popular teams are Barcelona, Manchester City, Real Madrid, and Chelsea; just to name a few. At the website above, choose a team and then go to “squad” and a list of the players on the team will appear. In this form the data is list and is in ungrouped form.

1. From here create a frequency distribution table for each month (January through December) and tally the number of players born in each month.
Answers will vary based on the team that the student chooses and the players on the team at that time. This is an example for Manchester United in July 2012.
Month Frequency
January 5
February 2
March 2
April 2
May 1
June 1
July 2
August 2
September 1
October 1
November 6
December 2
2. Then calculate the mean number of players born in a given month.
The mean number of players born in a given month is 2.25 players.

Soccer player.

### Extension Investigation

Let investigate the birth months more to determine if there is a trend!

1. What is the mode number of players born in a given month? The mode is 6 and that is in the month of November.
2. What is the median number of players born in a given month? The median number of players in a given month is 2.
3. What is the range of for the number of players born in a given month? The range is 5.
4. What measure of central tendency do you think is the most useful for analyzing the birth month of professional soccer players? Explain. The mean is very useful as it indicates that the majority of the months have 1 or 2 players born in that month, but there are a few outliers.
5. What trends do you notice in the birth months of professional soccer players? Explain. In the months of November and January there are a significantly larger number of players than in the other months. In addition between the months of November and April there are more than twice as many players born than the number of players born between the months of May and October.
6. Give a hypothesis for the reason that the trends exist! Explain. Based on this information, I wonder if the cut of month for competitive soccer leagues in Europe is November. This would explain why a significantly higher portion of the players were born in the months after November.

Further extension: create a bar graph to represent the number of players born in each month. Scan or upload your graph to the CK-12 website!

### Connections to other CK-12 Subject Areas

• Mean
• Mean of Grouped Data
• Measures of Central Tendency and Dispersion
• Mode
• Median
• Bar Graph

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