Definition

A branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters.

Basic terms

Mean: the sum of observations divided by the number of observations. For normal distributions, the mean is the better measure of central tendency as it does not fluctuate with the sample.

Median: the value which divides the observations into two equal halves when they are arranged in order of increasing value.

Mode: themost frequently occurring value in a distribution. It fluctuates with the sample and many distributions have more than one mode, hence it should not be used on its own.

Range: the difference between the largest and smallest values.

Percentiles: these divide a data set into 100 equally sized groups

Interquartile range: the difference between the 75th percentile and the 25th percentile.

Standard deviation (SD): can be regarded as being approximately equal to the average distance each individual lies away from the sample mean. 68% of the data will lie between 1 SD on each side of a normal distribution. 95.4% of the data will lie between 2 SDs and 99.7% between 3SDs.

Variance: a measure of how spread out a distribution is. It is equivalent to the standard deviation squared.

Standard error of themean(SE): the standard deviation of the subgroup gives a statistic that determines the spread of that subgroup. However, often it is useful to know how variable the means of a number of such subgroups would be so that the range over which the mean of the whole population lies can be assessed without actually taking measurements on the entire population.