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Explain the divergence from normality


In a frequency polygon or histogram of test scores, usually the first thing that strikes one is the symmetry or lack of it in the shape of the curve. In the normal curve model, the mean, the median and the mode all coincide and there is perfect balance between the right and left halves of the curve. Generally two types of divergence occur in the normal curve.

1) Skewness

2) Kurtosis

1) Skewnes: A distribution is said to be “skewed” when the mean and median fall

at different points in the distribution and the balance i.e. the point of center of gravity is shifted to one side or the other to left or right. In a normal distribution the mean equals, the median exactly and the skewness is of course zero (SK = 0).

There are two types of skewness which appear in the normal curve.

a) Negative Skewness : Distribution said to be skewed negatively or to the left when scores are massed at the high end of the scale, i.e. the right side of the curve are spread out more gradually toward the low end i.e. the left side of the curve. In negatively skewed distribution the value of median will be higher than that of the value of the mean.

b) Positive Skewness: Distributions are skewed positively or to the right, when scores are massed at the low; i.e. the left end of the scale, and are spread out gradually toward the high or right end as shown in the 

2) Kurtosis: The term kurtosis refers to (the divergence) in the height of the curve, specially in the peakness. There are two types of divergence in the peakness of the curve

a) Leptokurtosis: Suppose you have a normal curve which is made up of a steel wire. If you push both the ends of the wire curve together. What would happen in the shape of the curve? Probably your answer may be that by pressing both the ends of the wire curve, the curve become more peeked i.e. its top become more narrow than the normal curve and scatterdness in the scores or area of the curve shrink towards the center.

Thus in a Leptokurtic distribution, the frequency distribution curve is more peaked than to the normal distribution curve.

b) Platykurtosis: Now suppose we put a heavy pressure on the top of the wire made normal curve. What would be the change in the, shape of the curve? Probably you may say that the top of the curve become more flat than to the normal.

Thus a distribution of flatter Peak than to the normal is known Platykurtosis distribution. When the distribution and related curve is normal, the vain of kurtosis is 0.263 (KU = 0.263). If the value of the KU is greater than 0.263, the distribution and related curve obtained will be platykurtic. When the value of KU is less than 0.263, the distribution and related curve obtained will be Leptokurtic.

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