Measures of central tendency are statistical measures that provide a single value to describe the center or central location of a dataset. They give an idea of the central or typical value around which the data tends to cluster. The three most commonly used measures of central tendency are the mean, median, and mode.

1. Mean:

• Definition: The mean, often referred to as the average, is calculated by summing up all the values in a dataset and then dividing the sum by the number of values.
• Formula:
  
  $\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}$

   

  Mean=Number of valuesSum of all values​

• Characteristics:
  • Highly sensitive to extreme values or outliers.
  • Requires interval or ratio level data for accurate calculation.
  • Provides a balanced measure when the data is symmetrical.

2. Median:

• Definition: The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
• Characteristics:
  • Less sensitive to extreme values or outliers compared to the mean.
  • Suitable for ordinal, interval, or ratio level data.
  • Provides a measure of central location that divides the dataset into two equal halves.

3. Mode:

• Definition: The mode is the value(s) that occur most frequently in a dataset. A dataset may have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).
• Characteristics:
  • Can be determined for nominal, ordinal, interval, or ratio level data.
  • May not be unique if multiple values have the same highest frequency.
  • Provides a measure of central tendency that indicates the most common or frequent value(s) in the dataset.

Comparison:

• Mean:
  • Uses all values in the dataset.
  • Affected by extreme values.
  • Requires interval or ratio data.
• Median:
  • Uses the middle value(s) in the ordered dataset.
  • Less affected by extreme values.
  • Suitable for ordinal, interval, or ratio data.
• Mode:
  • Uses the most frequently occurring value(s).
  • Not affected by extreme values.
  • Suitable for nominal, ordinal, interval, or ratio data.

Selection of Measure:

The choice of the appropriate measure of central tendency depends on the nature of the data, the level of measurement, and the research objectives:

• Use the mean for interval or ratio data when the distribution is approximately symmetrical and not affected by outliers.
• Use the median when the data is skewed or contains outliers, or when dealing with ordinal data.
• Use the mode for nominal or categorical data, or when identifying the most common value(s) in the dataset.

measures of central tendency provide valuable insights into the central or typical value of a dataset. By understanding the characteristics and appropriate use of the mean, median, and mode, researchers and analysts can make informed decisions and interpretations based on the nature and distribution of the data.