Statistics Mean, Median, Mode

Statistics

• Definition: A branch of mathematics dealing with data collection, analysis, interpretation, presentation, and organization.
• Purpose: To summarize data and draw conclusions, often using numerical methods.

Mean

• Definition: The average of a set of numbers.
• Calculation:
  • Sum all values in the dataset.
  • Divide by the number of values.
• Formula: Mean (μ) = (Σx) / n, where Σx is the sum of all observations and n is the number of observations.

Median

• Definition: The middle value in a dataset when arranged in order.
• Calculation:
  • If the number of observations (n) is odd, the median is the middle number.
  • If n is even, the median is the average of the two middle numbers.
• Example: For the dataset {3, 5, 7}, the median is 5. For {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6.

Mode

• Definition: The value that appears most frequently in a dataset.
• Characteristics:
  • A dataset may have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all.
• Example: In the dataset {1, 2, 2, 3, 4}, the mode is 2.

Range

• Definition: The difference between the highest and lowest values in a dataset.
• Calculation:
  • Range = Maximum value - Minimum value.
• Example: In the dataset {4, 8, 15, 16, 23, 42}, the range is 42 - 4 = 38.

Statistics

• Statistics is a branch of mathematics focused on the collection, analysis, interpretation, presentation, and organization of data.
• Its primary purpose is to summarize data and draw conclusions through numerical methods.

Mean

• The mean, or average, is calculated by summing all values in a dataset and dividing by the number of values.
• Formula: Mean (μ) = (Σx) / n, where Σx represents the total of all observations and n is the count of observations.

Median

• The median is the central value in a dataset when values are arranged in ascending or descending order.
• If the total number of observations (n) is odd, the median is the middle number; if n is even, it averages the two middle numbers.
• Example: For {3, 5, 7}, the median is 5; for {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6.

Mode

• The mode identifies the number that appears most frequently within a dataset.
• A dataset can be unimodal (one mode), bimodal (two modes), multimodal (multiple modes), or have no mode.
• Example: In the dataset {1, 2, 2, 3, 4}, the mode is 2.

Range

• The range measures the difference between the highest and lowest values in a dataset.
• Calculation: Range = Maximum value - Minimum value.
• Example: For the dataset {4, 8, 15, 16, 23, 42}, the range is 42 - 4 = 38.