Question

Using Step-Deviation Method, find the mean of the following distribution :

Class : 30 - 40, 40 - 50, 50 - 60, 60 - 70, 70 - 80, 80 - 90
Frequency : 10, 6, 8, 12, 5, 9.

Best Answer will be Brainliest!!​

Answer 1

AnswEr :

$\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-2}\cline{1-3}\cline{1-7}Class & 30-40 & 40-50 & 50-60 & 60-70 & 70-80 & 80-90\\\cline{1-7} Frequency &10&6&8&12&5&9&\cline{1-7}\cline{1-6}\end{tabular}$

$\rule{200}{2}$

$\bigstar\:\boxed{\Large\sf Mean= A+h\bigg(\dfrac{\sum\limits\: f_{i}\:d_{i}}{\sum\limits\: f_{i}}\bigg)}$

$\bf{\dag}\:\: \underline\textsf{where we have}\\\bullet\:\textsf{A = Assumed Mean}\\\bullet\:\textsf{h = Class Width}\\\bullet\:\sf{\sum\limits\: f_{i} = Sum \:of \:Frequencies}$

$\rule{400}{1}$

$\begin{array}{|c|c|c|c|c|}\cline{1-5}\sf Class\: Interval& \sf Frequency(f_{i})&\sf Class\: Marks(x_{i})&\sf d_{i}=\dfrac{(x_i-A)}{h}&\sf f_{i}d_{i}\\\cline{1-5}30-40&10&35&-3&-30\\40-50&6&45&-2&-12\\50-60&8&55&-1&-8\\60-70&12&\sf(A)=65&0&0\\70-80&5&75&1&5\\80-90&9&85&2&18\\\cline{1-5} \sf Total&\sf N=\sum\limits\: f_{i}= 50&&&\sf \sum\limits\: f_{i}d_{i}=-27\\\cline{1-5}\end{array}$

$\underline{\bigstar\:\textsf{Calculation of Mean :}}$

$:\implies\sf Mean= A+h\bigg(\dfrac{\sum\limits\: f_{i}\:d_{i}}{\sum\limits\: f_{i}}\bigg)\\\\\\:\implies\sf Mean=65 + 10 \bigg(\dfrac{ - 27}{50}\bigg)\\\\\\:\implies\sf Mean=65 +\cancel{10} \times \dfrac{(-27)}{\cancel{50}}\\\\\\:\implies\sf Mean=65 + \dfrac{(- 27)}{5}\\\\\\:\implies\sf Mean=65 + ( - 5.4)\\\\\\:\implies\sf Mean=65 - 5.4\\\\\\:\implies\boxed{\red{\sf Mean=59.6}}$

⠀

$\underline{\therefore\:\textsf{The Required Mean of distribution is \textbf{59.6}}}$

Answer 2

Answer:

hope this will help you