Statistics Formula

Statistics Formulas - Basic Statistics Formulas

Statistics as a whole is a set of concepts, rules and procedures that help us to analyze the given data.
In other words, Statistics help us to

  • • Organize numerical information in the form of tables, graphs, and charts.

  • • Understand statistical techniques underlying decisions that effect our lives and well-being

  • • Make informed decisions.

  • With the help of statistics, we are able to find measures of central values which gives a rough idea about where data points are centered. Mean, Mode and Median are three measures of central tendency.
    Measures of variability provide information about the degree to which individual scores are clustered about or deviate from the average value in a distribution.

    The four measures of dispersion are
    a) Range
    b) Mean deviation
    c) Variance
    d) Standard deviation.

    Statistic Formulas
    1. Mean = \[\bar x = \frac{{\sum {x_i}}}{N}\] \[\begin{gathered}
      {x_i} = {\text{terms given}} \hfill \\
      N = {\text{Total no}}{\text{. of terms}} \hfill \\
    \end{gathered} \]
    2. Median = M = $\left\{ {\begin{array}{*{20}{c}}
      {{{\left( {\frac{{n + 1}}{2}} \right)}^{{\text{th}}}}{\text{term}};\quad n\,{\text{is odd}}} \\
      {\frac{{{{\frac{n}{2}}^{{\text{th}}}}{\text{term}} + {{\left( {\frac{{n + 1}}{2}} \right)}^{{\text{th}}}}{\text{term}}}}{2};\quad n\,{\text{is even}}}
    \end{array}} \right.$
    3. Mode = M = The value which occurs most frequently
    4. Mean deviation = M.D. = $\frac{{\sum {\left| {{x_i} - M} \right|} }}{N}$ (from average deviation)
    5. Variance = ${\sigma ^2} = \frac{{{{\sum {\left( {{x_i} - \bar x} \right)} }^2}}}{N}$
    6. Standard deviation = $\sigma = \sqrt {{\text{variance}}} $
    $ = \sqrt {\frac{{{{\sum {\left( {{x_i} - \bar x} \right)} }^2}}}{N}} $