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Measures of Central Tendency

Statistics: Central Tendency

December 13, 2024

Teacher Paul

Imagine you’re organizing a survey to understand people’s favorite ice cream flavors. After collecting the data, how do you summarize it? This is where measures like mean, median, and mode come in handy. They help us make sense of numbers and identify trends.

Contents

Mean

Definition: The mean is the average of a set of numbers, calculated by dividing the sum of all values by the number of values.

Formula

Simply,

Example 1

Imagine you have five test scores: 80, 85, 90, 95, and 100. To calculate the mean:

  1. Add the scores:
  2. Divide the sum by the number of scores:

The mean score is .

Example 2

Suppose you’re splitting a ₱120 bill among 4 friends equally. The mean cost per person is:

  1. Total amount:
  2. Divide by the number of friends:

Each friend pays .

If the numbers are 10, 15, 20, 25, what is the mean?

Median

Definition: The median is the middle value of a dataset when arranged in ascending order. If there’s an even number of values, the median is the average of the two middle numbers.

Example 1

For the dataset :

  1. Arrange the numbers (already done).
  2. Find the middle value: is the median.

Example 2

For the dataset :

  1. Arrange the numbers (already done).
  2. Average the two middle values:

The median is .

What is the median of 5, 10, 15, 20, and 25?

Mode

Definition: The mode is the value that appears most frequently in a dataset. A dataset can have one mode, more than one mode, or no mode at all.

Example 1

For the dataset :

Example 2

For the dataset :

What is the mode of 4, 5, 5, 6, 7, 7?

Test Yourself

If the numbers are 12, 14, 18, 20, and 22, what is the mean?
What is the mean of 5, 10, 15, 20, 25?
What is the median of 3, 6, 9, 12, and 15?
Find the median of 2, 4, 6, 8, 10.
What is the mode of 2, 4, 4, 6, 6, 6, 8?
Identify the mode in the set: 7, 7, 8, 9, 10, 10, 10, 11
Calculate the mean of 2, 4, 6, 8, and 10.
Determine the median of 1, 3, 3, 6, 7, 8, 9.
What is the mode of 10, 12, 12, 14, 15, 15, 15, 16?

Additional Context

Why are measures of central tendency important?
They summarize large datasets into meaningful numbers, helping us understand trends and make decisions. For example, a teacher might use the mean score to evaluate class performance.
How are mean, median, and mode used in real life?
The mean is often used in economics (e.g., average income), the median is crucial in statistics to avoid skewed data (e.g., median home prices), and the mode helps identify trends (e.g., most popular product).
When should I use median over mean?
The median is more reliable when data includes outliers. For example, if one person in a group earns significantly more than others, the median income provides a better measure of central tendency.
How can I improve my understanding of Mean, Median, and Mode?
Practice with real data sets, use educational apps and games, and try to apply these concepts to situations in your daily life. Regular practice and application will help solidify your understanding.

Key Takeaways