Normal distribution

Normal distribution

A variable graphically described with a bell-shaped density curve. The location and spread of the curve are dictated by the mean and standard deviation of the distribution. With a standard normal distribution, the peak of the bell curve will be at the mean and almost all values will fall between three standard deviations of the mean.

 

If a variable has a normal distribution, the bell curve will be visually evident with a large enough sample. For example, a meal may normally be distributed to contain 200 calories, with a standard deviation of 5 calories. With a small dataset of just three or four observations there is more susceptibility to outliers (on either side) skewing the distribution, however as the sample size grows the bell shape will become more sharp and symmetric.

 

While the normal distribution can often be useful for describing population distributions, it can also be very useful when working with sampling distributions. The sampling distribution of the sample mean can be estimated by a normal distribution and this works regardless of the shape of the population. As sample sizes increase, the sampling distribution will become more ‘normal’ as the outliers have less significance on the overall distribution.