NORMAL CURVE AND ITS APPLICATIONS
Normal
Probability Curve
Normal probability curve is an ideal symmetrical
frequency curve and is supposed to be based on the data of a population. Normal probability curve is bell shaped curve
and a graph representing a distribution of scores.
Figure 1.
Normal probability curve
Characteristics
·
It is bell shaped curve.
·
It is symmetrical the percentage of frequencies is the
same for equal intervals below or above the mean.
·
The curve never touches the base line(x axis).
·
The values of mean, medium and mode all coincide.
·
It is a asymptotic i.e. a line that continually
approaches a given curve but does not meet it at any finite distance.
·
The normal curve involves a continuous distribution.
·
The normal curve has only one mode.
Applications
of Normal Probability Curve
There are a
number of applications of normal probability curve especially in the field of
educational research.
§ To convert raw
score into standard scores.
§ To calculate the
percentile rank of scores.
§ To normalize a
frequency distribution. It is an important
step in standardizing a psychological test or inventory.
§ To test the
significance of observations in experiments, findings their relationships with
the chance fluctuations or errors that are the result of sampling procedures.
§ To generalize
about population from which the samples are drawn by calculating the standard
error of mean and other statistics.
Merits and demerits of normal distribution. Following are the merits and demerits of Normal
Distribution.
Merits. Following are the merits of Normal Distribution.
·
Normal distribution is the mostly used distribution in
inferential statistics.
·
The normal distribution has a number of mathematical
properties.
·
Most of errors of measurements and a large variety of
physical observations have approximately normal distributions.
·
The standard Normal distribution table shows
exhaustively areas for the different intervals of the values of the variables.
Demerits. Following are the merits of
Normal Distribution.
§ The Normal
distribution cannot be applied to situations where the distribution is highly
skewed.
§ The variables
which are not continuous cannot be normally distributed.
Table 1
Area of curve
falls between standard deviation
No
|
Standard deviation
|
Area %
|
1
|
-1 to +1
|
68.26
|
2
|
-2 to +2
|
95.44
|
3
|
-3 to +3
|
99.73
|
Video of Applications of Normal Curve
