ABSTRACT
A sample statistic is any quantity derivable from the observed values of a random variable, for example, the proportion of smokers in a sample of students is itself a random variable since its value will change from sample to sample. In the case of a parent distribution with perfect symmetry, the mode, median and mean for the population coincide. When the distribution is skew either positively or negatively, the mean lies away from the median in the direction of the long ‘tail’ of the distribution. The statistic that is usually used in such circumstances is the interquartile range – simply the difference between the 75th and 25th percentiles. For data grouped into classes, statisticians can also provide a rough indication of the location of a frequency distribution by finding the ‘most popular class’, that is, the point below the highest peak of the frequency polygon.
