Question

If a, b, c are the midvalues of classes and a, b, c are their frequencies respectively then
what is the A.M ?​

Answer 1

GiveN :-

• a, b, c are the midvalues of classes and a, b, c are their frequencies respectively .

To FinD :-

• The Arthemetic Mean .

SolutioN :-

As we know that the mean of group data is calculated by Firstly finding the Class Mark (x¡) and then Multiplying it with the respective frequency of that class interval . Then after adding all those ( f¡ × x¡ ) , we divide it with the sum of all frequency .

Here we are already given the class Mark as mid value of the classes a , b and c respectively and their respective Frequencies as a , b and c .

$\red{\bigstar}\underline{\textsf{ Constructing a Frequency distribution table :- }}$

$\boxed{\begin{gathered}\begin{array}{c|c|c} \underline{\red{\sf Class \ Mark }} & \underline{\red{\sf Frequency }}&\underline{\red{ \sf (f_i \times x_i ) }} \\ \sf a & \sf a &\sf a^2\\\sf b & \sf b&\sf b^2 \\\sf c & \sf c &\sf c^2 \\\\\sf & \sf \sum f_i = (a+b+c) &\sf \sum(f_i\times x_i = (a^2+b^2+c^2) \end{array} \end{gathered}}$

Hence the mean will be ,

$\sf:\implies\underset{\blue{\sf Required \ AM }}{\underbrace{\boxed{\pink{\frak{ AM = \dfrac{a^2+b^2+c^2}{a+b+c} }}}}}$