Mean

Arithmetic Means

If the total sum observation is divided by a total number of observations, then it is called arithmetic mean. It is denoted by \(\overline{X}\) (Read as X-bar)
∴ Arithmetic Mean = \(\frac{Total\;sum\;of\;observation}{Total\;no.\;of\;observation}\)
For example,
Arithmetic mean of 1, 3, 7, 11, & 13

= \(\frac{1+3+7+11+13}{5}\)
= \(\frac{35}{5}\)
= 7

1. Calculation of Mean for individual series
   The mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.
   If x₁, x₂, x₃, …………..x_n are be n variants value of variable a. Then arithmetic mean is denoted by \(\overline{X}\)
   So, \(\overline{X}\) = \(\frac{x_1+ x_2+ x_3+ …………..x_n}{n}\) = \(\frac{∑X}{n}\)
   Where ∑X = sum of n observation or items
   n = no. of observations or items
   X = variable
   
   
2. Calculation of Mean for discrete series
   Mean for discrete series can be calculated by
   \(\overline{X} = \frac{sum\;of\;the\;product\;of\;f\;and\;x}{sum\;of\;f}\)
   = \(\frac{∑fx}{N}\)
   
   
3. Calculation of Mean for continuous series
   For calculating mean in continuous series the following formulae is used:
   \(\overline{X}\) = A + \(\frac{∑fx}{N}\) × i
   where, F = Frequency and A = mid-value