Download Concepts in Probability - Glasgow Independent Schools

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Probability amplitude wikipedia, lookup

Law of large numbers wikipedia, lookup

History of statistics wikipedia, lookup

Inductive probability wikipedia, lookup

Foundations of statistics wikipedia, lookup

Bell Curve, Normal Distribution Defined
Definition: The term bell curve is used to describe the mathematical concept called
normal distribution, sometimes referred to as Gaussian distribution. ‘Bell curve’ refers to
the shape that is created when a line is plotted using the data points for an item that meets
the criteria of ‘normal distribution’. The center contains the greatest number of a value
and therefore would be the highest point on the arc of the line. This point is referred to
the mean, but in simple terms it is the highest number of occurences of a element. (
statistical terms, the mode). The important things to note about a normal distribution is
the curve is concentrated in the center and decreases on either side. This is significant in
that the data has less of a tendency to produce unusually extreme values, called outliers,
as compared to other distributions. Also the bell curve signifies that the data is symetrical
and thus we can create reasonable expectations as to the possibility that an outcome will
lie within a range to the left or right of the center, once we can measure the amount of
deviation contained in the data . These are measured in terms of standard deviations. A
bell curve graph depends on two factors, the mean and the standard deviation. The mean
identifies the position of the center and the standard deviation determines the the height
and width of the bell. 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’:
1. The total area under the curve is equal to 1 (100%)
2. About 68% of the area under the curve falls within 1 standard deviation.
3. About 95% of the area under the curve falls within 2 standard deviations.
4 About 99.7% of the area under the curve falls within 3 standard devations.
Items 2,3 and 4 are sometimes referred to as the ‘empirical rule’ or the 68-95-99.7 rule.
In terms of probability, once we determine that the data is normally distributed ( bell
curved) and we calculate the mean and standard deviation, we are able to determine the
probability that a single data point will fall within a given range of possibilities.