Interpreting Normal Distribution

To determine the unusual state of a population in a normal distribution, it is important to first of calculating the z-score of the total population. It is usually given as follows; 

Z-score = , whereby; 

X= value to be standardized 

µ= mean 

β= standard deviation, therefore our z-score will be determined as follows; 

= 1. 732050807568 or 1.732 

As such, the z-score of 1.732 lies within 3 standard deviations meaning the normal distribution of the population is not unusual at all. 

Sum of squares is a statistical technique that was developed to determine how dispersion of data in a given population distribution. It is mainly applied in regression analysis, in the determination of standard deviation, variance, and analysis of variance. The sum of squares is significant in the statistical analysis it determines the least variable series of data or the best-fit series of data from a given population distribution. To determine the sum of squares, the mean of the given series of data is subtracted from the values to be standardized and their squares summed up. Statistical calculations and analysis should be based on a sum of squares since this technique provide data which has a minimal variation and at the same time reduces. The sum of squares is applied when measuring data involving bank interest rates, inflation, and earthquakes level since through this technique; it is possible to determine a least variable data series even though the data that is usually present in such activities has a wide variation. However, through the sum of squares method, statisticians can manipulate the data and achieve the best-fit series data. This data is helpful since it is used to determine future bank interest rates, inflation rates and earthquake levels and radioactive decay levels ( Everitt, 2006). 

The logic behind statistical analysis using statistical techniques such as the mean, standard deviation, variance and normal curve concept is measuring the distribution or spreading of data within a given series of data. In most cases, the standard deviation, the mean and normal curve are applied to estimate the distance a particular set of data is from the mean ( Everitt, 2006). 

References 

Everitt, B. S. (2006).    The Cambridge dictionary of statistics . Cambridge University Press.