Definition

1. Noun:
   • A measure of central tendency: The arithmetic mean is the most common type of average. It is calculated by adding together all the numbers in a set of values and then dividing that sum by the total count of values in that set.

Usage

• The arithmetic mean provides a single value that summarizes the central point of a data set.
• It is used extensively in statistics, mathematics, economics, and everyday life to find a typical value.
• It is often simply called the "average," though other types of averages (like the median and mode) exist.

Examples

• Noun:
  • To find the arithmetic mean of 5, 10, and 15, you calculate (5+10+15)/3, which equals 10.
  • The arithmetic mean of the test scores gave the teacher a good idea of the class's overall performance.
  • Investors often look at the arithmetic mean return over a period to assess an asset's performance.

Advanced Usage

• "Population arithmetic mean": The average calculated using every member of a defined group (population).
  • The population arithmetic mean income for the country was calculated from census data.
• "Sample arithmetic mean": The average calculated using a subset (sample) taken from a larger population.
  • The researcher reported the sample arithmetic mean from the survey responses.

Variants and Related Words

• Mean (n): A common short form for "arithmetic mean."
  • The mean of the data set was 24.5.
• Average (n): A general term often used synonymously with the arithmetic mean, though it can refer to other measures of central tendency.
  • The average temperature for July was higher than usual.

Synonyms

• Average: The general term for a number expressing the central value in a data set.
• Mathematical expectation (in probability): For a discrete random variable, this is equivalent to its arithmetic mean.

Related Concepts (Not Phrasal Verbs or Idioms)

• Median: The middle value in a list of numbers sorted in ascending order.
• Mode: The value that appears most frequently in a data set.
• Weighted mean: An average where some data points contribute more than others.

Noun

1. the sum of the values of a random variable divided by the number of values