Parameters in statistics is an important component of any statistical analysis. In simple words, a
parameter is any numerical quantity that characterizes a given population or some aspect of it.
This means the parameter tells us something about the whole population.
A parameter never changes, because the whole population was surveyed to find the parameter (will be
independent of the variable and the number of cases that are taken to study). The most common
statistics parameters are the measures of central tendency(mean, median, and mode). These tell us how
give us an idea about where the data concentrates. Standard deviation tells us how the data is spread
from the central tendency, i.e. whether the distribution is wide or narrow. Such parameters are often
very useful in analysis.
In the normal distribution, there are two parameters that can characterize a distribution - the mean and
standard deviation. By varying these two parameters, you can get different kinds of normal
distributions.
The density of the normal distribution (the height for a given value on the x axis) is shown
below. The parameters μ and σ are the mean and standard deviation, respectively, and define the
normal distribution. The symbol e is the base of the natural logarithm and π is the constant pi.
Descriptions of Normal Distribution:
Shaped like a bell; the curve peaks at the middle and slopes downward away from the mean
Normal distributions are symmetric around their mean. The mean, median, and mode of a
normal distribution are equal. The area under the normal curve is equal to 1.0. Normal
distributions are denser in the center and less dense in the tails. Normal distributions are
defined by two parameters, the mean (μ) and the standard deviation (σ). More than half of
the total area under the curve (68%) is within one standard deviation of the mean.
Approximately 95% of the area of a normal distribution is within two standard deviations of
the mean.