summary

Central Tendency

• Definition: Central tendency refers to the statistical measures that identify a single value as representative of an entire set of data.

• Three Measures of Central Tendency:

  • Mean:

  • Definition: The mean is the arithmetic average of a set of data. It is calculated by summing all values in a dataset and dividing by the number of values.

  • Formula:
    ext{Mean} (ar{x}) = rac{ ext{Sum of all values}}{ ext{Number of values}}

  • Median:

  • Definition: The median is the middle value of a dataset when the numbers are arranged in ascending or descending order. If the dataset has an even number of values, the median is the average of the two middle numbers.

  • Calculation Steps:

    1. Arrange the data in order.

    2. If the number of observations (n) is odd, the median is the value at position rac{n + 1}{2}.

    3. If n is even, the median is the average of the values at positions rac{n}{2} and rac{n}{2} + 1.

  • Mode:

  • Definition: The mode is the value that appears most frequently in a dataset. A dataset may have one mode, more than one mode (bimodal or multimodal), or no mode at all.

Variability

• Definition: Variability measures how spread out or how far apart the numbers in a dataset are from one another. It indicates the extent of variation in the data points.

• Measures of Variability:

  • Range:

  • Definition: The range is the difference between the largest and smallest numbers in a dataset. It provides a simple measure of how much the values differ.

  • Formula:
    ext{Range} = ext{Maximum Value} - ext{Minimum Value}