Definition

Noun: A symmetrical, bell-shaped curve that graphically represents the normal distribution in statistics. It is characterized by its mean, median, and mode being equal and located at the center, with specific proportions of data falling within standard deviations from the mean.

Usage

The term "normal curve" is used in statistics, data science, psychology, and other fields to describe the expected distribution of many natural phenomena and measured variables. It serves as a fundamental model for probability and statistical inference.

Examples

• The test scores formed a perfect normal curve, with most students scoring near the average.
• When plotting the data, the researcher observed that it closely followed a normal curve.
• In a normal curve, approximately 68% of the data falls within one standard deviation of the mean.

Advanced Usage

• "To approximate a normal curve": When data distribution is very close to, but not perfectly, the ideal bell shape.
  • With a large enough sample size, the sampling distribution will approximate a normal curve.
• "Under the normal curve": Referring to the area or probability within the distribution.
  • The shaded area under the normal curve represents the probability of that outcome.

Variants and Related Words

• Normal distribution (n): The theoretical probability distribution that the normal curve represents. Often used interchangeably with "normal curve," though "distribution" refers more to the function and "curve" to its graph.
• Bell curve (n): A common synonym for "normal curve," emphasizing its shape.
• Gaussian curve (n): A less common synonym, named after the mathematician Carl Friedrich Gauss.

Synonyms

• Bell curve
• Gaussian curve

Related Phrases

• Standard normal curve: A specific normal curve with a mean of 0 and a standard deviation of 1.
  • We converted the scores to z-scores to plot them on the standard normal curve.

Noun

1. a symmetrical curve representing the normal distribution