Normal Distribution of Frequency in the Histogram

The frequency distribution in the histogram was obtained from 200 measurements segregated into seven classes, each class having a 'width' of 5 mg. If a very much larger number of measurements were made and classified into a much larger number of 'narrower' classes, a smoother profile, approximating to this figure might be expected. This symmetrical, bell-shaped distribution is known as the normal distribution, and the outputs of many business processes conform to it. This is useful because the properties of the normal distribution are well-defined, allowing predictions to be made of the proportion of the output population which will lie within a specified measurement range. It should be noted that any particular normal distribution is completely specified by its µ and σ values. The setting of the process in relation to the relevant product design tolerance band is indicated by the mean, µ. The dispersion of the output about the mean is indicated by the standard deviation, σ: the larger the standard deviation, the flatter the bell shape.

Statistical control of such a process is concerned with detecting the effects of assignable causes of variability on the process mean and standard deviation.