Answer to Question #100810 in Statistics and Probability for Jiya

Question

In finding arithmetic mean of ungrouped Data by shortcut method(deviation method) . the formula is =a+ (sum of D) /n where D=X-a.. Here a is assumed mean.. How to find assumed mean?

Answer 1

In derivation method the mean is given by,

$mean =a+ \frac{\Sigma (x-a) }n \newline$

Assumed mean is an arbitrary constant which is used to simplify the calculation,meaning guess or an assumption of the mean. Assumed mean is most commonly denoted by the letter a.

It doesn't need to be correct or even close to the actual mean.

The choice of the assumed mean is at your discretion, except for where the question explicitly asks you to use a certain assumed mean value.

For most cases arrange the ungrouped data in ascending order then,if the number of observations is even then take assumed mean =$(\frac{n}{2}+1)^{th}$ observation

if number of observation is odd then take assumed mean as=$(\frac{n+1}{2})^{th}$ observation