Measures

Measures

1. measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

   • So, if we have n values in a data set and they have values x1, x2, ..., xn, the sample mean, usually denoted by (pronounced x bar), is:

2. The measures of central tendency are not adequate to describe data. Two data sets can have the same mean but they can be entirely different. Thus to describe data, one needs to know the extent of variability. This is given by the measures of dispersion. Range, interquartile range, and standard deviation are the three commonly used measures of dispersion.

   • Example In both these formulas n - 1 is used instead of n in the denominator, as this produces a more accurate estimate of population SD. The reason why SD is a very useful measure of dispersion is that, if the observations are from a normal distribution, then[3] 68% of observations lie between mean ± 1 SD 95% of observations lie between mean ± 2 SD and 99.7% of observations lie between mean ± 3 SD

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