Score! with Statistics

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Refresh learners’ memory on the measures of central tendency: Mean, Mode, and Median.

Additional information for teachers:

Let's take an example to understand this better. Imagine you have the following numbers: 5, 8, 4, 2, 9. To find the mean, add up all these numbers: 5 + 8 + 4 + 2 + 9 = 28. Next, you divide this sum by the total number of values in the set, which is 5. So, 28 ÷ 5 = 5.6. Therefore, the mean of this set of numbers is 5.6.

The mean is helpful because it gives us a representative value that summarizes the entire set. It helps us understand the average or typical value in the data. For example, if we were looking at the mean score of a class on a test, it would give us an idea of how well the class performed on average.

However, it's important to note that extreme values can influence the mean in the data. For instance, if one learner in a class scores much higher or lower than everyone else, it can significantly impact the mean. That's why it's essential to consider other measures of central tendency, like the median and mode, which provide additional information about the data.

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Additional information for teachers:

Let's consider an example to understand this better. Imagine you have the following set of colors representing the favorite colors of learners in a class: red, blue, blue, green, yellow, blue, red, purple, and blue. To find the mode, we identify the color that occurs most frequently. In this case, "blue" appears four times more than any other color. Therefore, the mode of this set of data is "blue."

In summary, the mode is the value or values that occur most frequently in a data set. It helps us identify the data set’s most common or popular value. The mode provides insights into the prevailing characteristic of the data.

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Additional information for teachers:

Let's look at an example to understand this better. Imagine you have the following set of numbers representing the ages of learners in a class: 10, 12, 13, 14, 15, 16, 17. To find the median, we first arrange the numbers in order: 10, 12, 13, 14, 15, 16, 17. Since the data set has an odd number of values (7), the median is the middle value. In this case, the middle value is 14. Therefore, the median of this set of data is 14.

The median is applicable because it represents the value that splits the data into two halves. It gives us an idea of the "typical" value in the data set, which is not influenced by extreme values. For example, if we were looking at the median income of families in a neighborhood, it would indicate the income level in the middle, without being influenced by extremely high or low incomes.

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Begin by sharing that they will get to know their classmates better by conducting a fun survey and then calculating the data's mean, mode, and median. 

Distribute the survey to each group. 

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The Survey Sheet will be divided into three main sections: 

• Data collection, 
• Calculations, 
• Analysis.

In the data collection section, learners will write down the responses they gather from their classmates for questions such as "How many hours of sleep do you get?", "How many hours do you play?", and "How many hours do you read?".

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To facilitate Data Collection and movement in the classroom, you can opt for the speed dating technique. 

Speed Dating:

1. Arrange chairs in two rows facing each other, creating a "speed dating" setup.
2. Half of the groups sit in one row, and the other half in the opposite row.
3. Assign one group as the "questioners" and the other as the "responders."
4. Give each group a set amount of time (e.g., 1-2 minutes) to ask and answer survey questions.
5. Instruct the groups to rotate positions after each round, allowing everyone to have a chance to ask and answer questions.
6. Learners record the responses on their worksheets as they interact with different peers during the activity.

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After collecting the data, learners will transition to the calculations section of the worksheet. They will come back and sit in groups, where they will calculate the mean, mode, and median based on the data they have collected. 

For learners to calculate the Mean, Mode, and Median of the data they collected from peers, provide 8 minutes. You can also set up a timer on the screen. 

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Ask learners where the measures of central tendency could be utilized in real life. Invite learners to share responses as a class.

Possible use cases could include:

1. Salary Analysis: In HR and job market research, the mean and median salaries are often calculated to understand the average or typical earnings in a particular occupation or industry. This information helps job seekers negotiate salaries and assists organizations in setting competitive compensation packages.
2. Customer Satisfaction Surveys: When analyzing customer satisfaction surveys, the mode is often used to identify the most common rating or feedback provided by customers. This helps businesses focus on improving specific areas that may negatively impact customer satisfaction.
3. Stock Market Analysis: Investors and financial analysts use stock price’s mean and median values to analyze trends and make investment decisions. These measures help identify the average performance of a stock or sector and assess potential risks or opportunities.
4. Response Time Analysis: In customer service or technical support, measures of central tendency, such as mean or median response times, are calculated to evaluate the efficiency of the support team. These measures help identify areas for improvement and ensure timely and satisfactory customer service.

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Share that over 1.5 billion people watched the 2022 World Cup Finals between Argentina and France. (In comparison, 115.1 viewers watched the last Super Bowl.) Ask learners:

• Who they think won, and why;
• If they think there is a way to predict the winner of the finals based purely on the historical statistics of players from the different teams.

Show the video to introduce learners to soccer. Conclude by sharing that Argentina and France drew 3-3, but Argentina won 4-2 on penalties.

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Introduce learners to the task by posing the question on the slide: Do you watch soccer or any other sport? How does ESPN or other commentators determine the odds of a winning team?

Possible learner responses:

• They might examine the team's previous records and performance to predict the outcome.
• I think they analyze the players' skills and statistics to see how they match up against each other.
• They may consider the head-to-head history between the teams to see if there are any patterns or trends.
• They also consider the team's form or recent performance leading up to the game.

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Share that measures of central tendency help to optimize team performance in sports. 

Additional information for teachers:
Data analysis plays a crucial role in sports, including soccer, for several reasons:

1. Performance Evaluation: Data analysis allows coaches, analysts, and teams to objectively assess player and team performance. By analyzing various statistics such as goals scored, assists, shots on target, passing accuracy, and defensive actions, they can identify strengths and weaknesses, make informed decisions, and devise effective strategies for improvement.
2. Tactical Insights: Data analysis helps teams uncover patterns and trends in gameplay, providing valuable insights into opponents' strategies and weaknesses. By analyzing data from past matches, teams can identify opponent patterns, formations, and player tendencies, enabling them to develop tactical approaches and game plans to exploit these insights.
3. Player Recruitment and Scouting: Data analysis assists in player recruitment and scouting processes. By analyzing performance data, teams can identify talented players, assess their suitability for specific positions, and make informed decisions when acquiring new players. Metrics such as goals, assists, pass completion rates, and defensive actions comprehensively overview a player's abilities and potential.
4. Injury Prevention and Player Conditioning: Data analysis helps monitor player fitness levels, workload, and risks. By analyzing training and match data, teams can optimize player conditioning programs, track fatigue levels, identify injury-prone players, and implement preventive measures to reduce the risk of injuries.
5. Strategy and Decision-Making: Data analysis supports strategic decision-making during matches. Real-time data analysis, such as player positioning, ball possession, passing patterns, and shot locations, allows coaches and analysts to make informed decisions on substitutions, tactical adjustments, and game strategies to maximize the team's chances of success.

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Apprise learners of the task. Share that they will receive a Soccer Statistics data set comprising different soccer teams and the performance of their players for the last couple of matches. The sample data has the following details:

• Minutes played
• Total goals
• Total assists
• Yellow card
• Red card
• Shots-per game
• Pass success percentage
• Aerial duels won per game
• Man of the match
• Height (in feet/inches)
• Weight (in lbs)

Learners will calculate the mean, mode, and median of different teams on Google Sheets and choose the most likely to win a tournament. They will back their insights with relevant data.

Duplicate the sheet and share a different copy with every team. Alternatively, request learners to go to File >> Make a Copy to duplicate the sheet and work on separate copies.

Distribute copies of the “My Winning Team” worksheet to learners. Instruct learners to refer to the worksheet for guiding questions and fill it in according to their analysis.

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Learners can go through the video tutorial to calculate how to find out mean, mode and median.