1. Arithmetic Average in Individual Series
Direct Method
\[\bar{X} = \frac{\sum X}{N}\]
Where;
= Arithmetic Mean
\(\sum {X}\) = Sum of all values
= Total number of observations
Shortcut Method
\[\bar{X} = A + \frac{\sum d}{N}\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
\(\sum {d}\) = Sum of all deviations
= Total number of observations
Step Deviation Method
\[\bar{X} = A + \left( \frac{\sum d’}{N} \right) \times c\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
= 
\(\sum {d’}\) = Sum of deviations ()
= Common factor
= Total number of observations
2. Arithmetic Average in Discrete Series
Direct Method
\[\bar{X} = \frac{\sum fX}{\sum f}\]
Where;
= Arithmetic Mean
\(\sum {fX}\) = Total of products of the frequencies and the variable X
\(\sum {f}\) = Total of frequencies
Shortcut Method
\[\bar{X} = A + \frac{\sum fd}{\sum f}\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
\(\sum {fd}\) = Total of products of the frequencies(
) and the deviations (
) of the values of variables from an assumed mean ()
= Total number of observations
Step Deviation Method
\[\bar{X} = A + \left( \frac{\sum d’}{\sum f} \right) \times c\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
=
\(\sum {d’}\) = Sum of deviations ()
= Common factor
= Total number of observations
3. Arithmetic Average in Continuous Series
Direct Method
\[\bar{X} = \frac{\sum fm}{\sum f}\]
Where;
= Arithmetic Mean
= mid-point
\(\sum {fm}\) = Total of products of the frequencies and the mid-points
\(\sum {f}\) = Total of frequencies
Shortcut Method
\[\bar{X} = A + \frac{\sum fd}{\sum f}\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
\(\sum {fd}\) = Total of products of the frequencies() and the deviations () of the values of variables from an assumed mean ()
= Total number of observations
Step Deviation Method
\[\bar{X} = A + \left( \frac{\sum d’}{\sum f} \right) \times c\]
Where;
= Arithmetic Mean
= Assumed Mean
= Deviation of each value
= 
\(\sum {d’}\) = Sum of deviations ()
= Common factor
= Total number of observations