Now the sample mean will vary from sample to sample the way this variation occurs is described by the вЂњsampling distributionвЂќ of the mean. We usually collect data in order to generalise from them and so use the sample mean as an estimate of the mean for the whole population.

When we calculate the sample mean we are usually interested not in the mean of this particular sample, but in the mean for individuals of this type-in statistical terms, of the population from which the sample comes. We may choose a different summary statistic, however, when data have a skewed distribution. About 95% of observations of any distribution usually fall within the 2 standard deviation limits, though those outside may all be at one end. Contrary to popular misconception, the standard deviation is a valid measure of variability regardless of the distribution. For data with a normal distribution, 2 about 95% of individuals will have values within 2 standard deviations of the mean, the other 5% being equally scattered above and below these limits. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn. The standard deviation (often SD) is a measure of variability. 1 The contrast between these two terms reflects the important distinction between data description and inference, one that all researchers should appreciate. The terms вЂњstandard errorвЂќ and вЂњstandard deviationвЂќ are often confused.

How calculate standard error