normal distribution

normal distribution(Gaussian distribution) The symmetrical bell-shaped frequency curve formed when the frequency of a range of values is plotted on the vertical axis against the value of a random variable on the horizontal axis. The bell shape indicates that extreme values (both large and small) occur infrequently, while the more frequent occurrences are clustered around the arithmetic mean value, which in a normal distribution is also equal to the median and the mode (the value that occurs most frequently in a set of data).

Normal distribution curve. Figure 1: the bell-shaped normal distribution curve.

A wide variety of natural, social, and economic phenomena fall approximately into a normal distribution, which is therefore an important concept in statistical analysis. From Figure 1 it can be seen that if a population is investigated, the range of values is six times the standard deviation (SD), i.e. almost all the values from the population lie within three SDs either side of the mean. For a normal distribution, one SD either side of the mean can be seen to cover 68% (34% + 34%) of observed values (or the area under the curve); for two SDs it covers 95%; and for three SDs it covers 99%.

The SD is important in marketing research as it provides the researcher with some idea of the range of answers to a question. In Figure 2 two sample populations, A and B, have the same mean, but population B has a greater SD than population A (indicated by the spread of the curve). While the researcher may have asked both populations the same questions, with both populations on average agreeing (i.e. the same mean), there is a greater dispersion in population B, indicating a greater variation of opinion than in A.

Figure 2: normal distribution curves having the same mean but different standard deviations.

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