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Monday, November 5, 2018

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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



Audio of applications of Normal Curve

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