Definition

1. Adjective:

   • Relating to or situated in the middle: "Median" describes something positioned at or extending toward the center point.
   • Dividing into two equal halves: In geometry or anatomy, "median" refers to a line or plane that divides something into symmetrical left and right halves.
   • Constituting the middle value: In statistics, "median" describes the central value in an ordered set of numbers, where half the numbers are greater and half are less.

2. Noun:

   • The middle value: In a set of numbers arranged in order, the "median" is the value separating the higher half from the lower half. For an even number of values, it is the average of the two middle numbers.
   • A central dividing line: In geometry, a "median" is a line from a vertex of a triangle to the midpoint of the opposite side. In anatomy, it can refer to a central structure, like a nerve or artery.

Usage Examples

• Adjective:

  • The median strip on the highway separates the lanes of traffic.
  • The median plane of the body divides it into left and right halves.
  • The median household income in the region has increased.

• Noun:

  • To find the median, first arrange the numbers in ascending order.
  • The median of the data set [3, 5, 7, 9] is 6.
  • In triangle ABC, line AD is the median from vertex A to side BC.

Advanced Usage

• "Median voter theorem": A principle in political science stating that under certain conditions, a candidate will adopt a policy position close to the median (middle) voter's preference to win an election.
• "Geometric median": A point that minimizes the sum of distances to a set of points, generalizing the concept of a median to multiple dimensions.

Variants and Related Words

• Medial (adj): Pertaining to the middle; often used in anatomy (e.g., the medial side of the knee).
• Medianly (adv): In a median position or manner (less common).
• Submedian (adj): Situated near but not exactly at the middle.

Synonyms

• Central: Located in the center.
• Middle: At an equal distance from the extremes.
• Mid: (Often used in compounds) Denoting the middle.
• Average (for the statistical noun, but note: "average" often means "mean," which is different).

Related Phrases

• Median nerve: A major nerve running down the arm, through the carpal tunnel.
• Median price: The middle price point in a sorted list of prices.
• Median filter: A digital filtering technique often used in image processing to reduce noise.

Idioms

(No common idioms are directly formed with the word "median." Its use is primarily technical and descriptive.)

Adjective

1. relating to or situated in or extending toward the middle
2. dividing an animal into right and left halves
3. relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values)
   • the median value of 17, 20, and 36 is 20
   • the median income for the year was $15,000

Noun

1. the value below which 50% of the cases fall