The below mentioned article provides a note on distribution pattern.
The frequency distribution and their graphical representation like frequency polygon, histogram, bar diagram. But sometimes the knowledge of distribution pattern is required to comment on the population on the basis of observation of sample.
Normal Distribution:
If we observe in any population any attribute is distributed mostly near the mean value and equally distributed to the higher and lesser value gradually in decreasing order then the distribution pattern is called normal distribution.
When this kind of normally distributed attribute is plotted graphically with the help of available data, the normal distribution pattern gives a bell shaped symmetrical curve which is called ‘normal distribution curve’. In this curve the mean value lies in the peak of the curve.
Properties of Normal Distribution Curve:
1. It is a continuous bell shaped curve which is associated with continuous variable.
2. There is only one maximum peak (unimodal). The normal curve is symmetrical (Fig. 10.1a) and asymptotic (touches at infinity).
3. The height of normal curve is maximum at its Mean. Mean, Median and Mode coincides in normal curve.
4. The peak divides the distribution in two equal halves.
5. Most of the observations are clustered around the Mean and there are relatively a few observations at the extremes.
6. The normal distribution curve has a fixed mathematical characteristic feature independent of the scale. (unit of measurement) of magnitude.
Skewness and Kurtosis:
In normal distribution, most of the cases fall in the middle but there are cases in which central tendency do not exhibit normal behaviour.
There are two types of divergence from normal distribution:
(i) Skewness and
(ii) Kurtosis.
(i) Skewness means that the curve is not symmetrical. In a skewed distribution, the Mean, Median and Mode do not coincide it pulls the Median and Mean away from Mode either left or right. In a skewed distribution, the frequency curve is not bell shaped and values do not lie on both sides of measure of central tendency equally. Here Mean Median and Mode fall at different points.
In symmetrical distribution curve, Mode coincides with Mean and Median. In positively skewed curve, the value of Mean and Median lie away from Mode values (right hand), the values are greater than Mode. In negatively skewed curve, the value of Mean and Median lie left hand to Mode value, the values are lesser than the Mode value (Fig. 10.1).
(ii) Kurtosis means the bulginess; it measures the degree of peakedness of a frequency distribution. In case of unimodal normal distribution, the peak has a flat top while the others may have peaked top. The degree of peakedness of a distribution is called as kurtosis.
We may have three kinds of kurtosis (Fig. 10.2):
1. Leptokurtic curve where the curve has high peak and long tails.
2. Mesokurtic curve which has moderately high peak comparable to the normal curve, peak is neither high nor flat.
3. Platykurtic curve when the curve has very flat top for its peak.
II. Dispersion:
In statistics, dispersion is commonly used to mean the scattering of data, deviation, fluctuation, spread or variability of data. The term ‘dispersion’ can be defined as the degree to which the individual values of the variate scatter away from the average or the central value.
Variability is a normal biological phenomenon, and it is important to measure this variability. This measurement helps us to find out how individual observations are dispersed around the mean of a large series. This is also named as measures of dispersion. 