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A bell-shaped curve, also known as a normal distribution or Gaussian distribution, is a symmetrical probability distribution in statistics. It represents a graph where the data clusters around the mean, with the highest frequency in the center, and decreases gradually towards the tails.
It is good to know the standard deviation, because we can say that any value is: The number of standard deviations from the mean is also called the "Standard Score", "sigma" or "z-score". Get used to those words! You can see on the bell curve that 1.85m is 3 standard deviations from the mean of 1.4, so:
The t-distribution forms a bell curve when plotted on a graph. It can be described mathematically using the mean and the standard deviation.
Some educators use the bell-shaped curve to determine students' grades, [3] and it is the basis for norm-referenced tests such as nationally used school tests and college entrance exams. The normal distribution has two descriptive measures: the mean and the standard deviation. [4] .
Due to its shape, it is often referred to as the bell curve: The graph of a normal distribution with mean of 0 0 and standard deviation of 1 1. Owing largely to the central limit theorem, the normal distributions is an appropriate approximation even when the underlying distribution is known to be not normal.
A smaller standard deviation indicates that the data is tightly clustered around the mean, resulting in a taller and thinner normal distribution. A larger standard deviation indicates that the data is spread out around the mean; the normal distribution will be flatter and wider.
All normal distributions, like the standard normal distribution, are unimodal and symmetrically distributed with a bell-shaped curve. However, a normal distribution can take on any value as its mean and standard deviation.
The term "bell curve" is used to describe a graphical depiction of a normal probability distribution whose underlying standard deviations from the mean create the curved bell shape.
For example, a large standard deviation creates a bell that is short and wide while a small standard deviation creates a tall and narrow curve. To understand the probability factors of a normal distribution, you need to understand the following rules: The total area under the bell curve is equal to 1 (100%).
Data that has this pattern are said to be bell-shaped or have a normal distribution. It can be shown that variables that arise as a result of the sum or average of a fixed number of individual smaller components of a similar nature will have this shape.