Key Points
1. Categorical data are non-numerical; discrete data can be listed; continuous data cn be measured to any degree of accuracy and it is not possible to list all values.

2. Stem-and-leaf-diagrams (or stemplots) are suitable for discrete of continuous data. All data values are retained as well as indicating properties of the distribution.

3. The mean, median, mode or modal class and the mid-range are measures of central tendency.
• The mean, xˉ = Σx ⁄ n; for grouped data xˉ = Σxf ⁄ n
• The median is the mid-value when the data are presented in rack order; it is the value of n + 1 ⁄ 2th item of n data items.
• The mode is the most common item of data. The modal class,?i> is the class containing the most data, when the calsses are of equal width.
• The mid-range = 1 ⁄ 2(minimum data value + maximum data value).

4. The range, mean square deviation, root mean square deviation, variance and standard deviation are measures of spread or dispersion.
• The range = maximum data value - minimum data value.
• the sum of squares Sxx = Σ(x - xˉ)2 or Σx2 - nxˉ2; for grouped data. Sxx = Σ(x - xˉ)2f or Σx2f - nxˉ2.
• The mean square deviation, msd = Sxx ⁄ n.
• The root mean square deviation, rmsd = √msd = √Sxx ⁄ n.
• The variance, s2 = Sxx ⁄ n - 1.
• The standard deviation, s = √variance = √Sxx ⁄ n - 1.

5. An item of data x may be identified as an outlier if |x - xˉ| > 2s; that is, if x is more than two standard deviations above or below the sample mean.

6. If data, represented by the variable x, are coded as y = a + bx, then the mean and standard deviation of the coded data are:
Mean of y = a + bxˉ and sy = bsx.

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