Question

Find Arithmetic Mean of the frequency distribution of monthly wages of 100 workers of a company. Wages (in Rs. ‘000) 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80 No of workers 6, 16, 27, 23, 16, 10, 2

Answer 1

See the attached fil

Answer 2

Answer:

$\begin{tabular}{|c|c|c|c|c|c|c|c|}\cline{1-8}Wages &10-10 & 20-40 & 30-40 & 40-50 & 50-60 &60-70&70-80\\\cline{1-8}Workers&6&16&27&23&16&10&2\\\cline{1-8}\end{tabular}$

$\begin{tabular}{|c|c|c|c|}\cline{1-4}Class Interval& Frequency&Mid-Term&\sf F_{\sf i}\sf X_i\\\cline{1-4}10 - 20 &6&15&90\\\cline{1-4}20 - 30 &16&25&400\\\cline{1-4}30 - 40 &27&35&945\\\cline{1-4}40 - 50 &23&45&1035\\\cline{1-4}50 - 60 &16 & 55&880\\\cline{1-4}60 - 70&10&65&650\\\cline{1-4}70 - 80&2&75&150\\\cline{1-4}Total&100&&4150\\\cline{1-4}\end{tabular}$

$\rule{150}{2}$

$\underline{\bigstar\:\textsf{Arithmetic Mean of Distribution :}}$

$\dashrightarrow\sf\:\:Arithmetic\:Mean=\frac{\textsf{Sum of Frequency and Mid Term}}{\textsf{Sum of Frequency}}$

$\\\dashrightarrow\sf\:\:Arithmetic\:Mean=\dfrac{f_i x_i}{f_i}\\\\\\\dashrightarrow\sf\:\:Arithmetic\:Mean=\dfrac{4150}{100}\\\\\\\dashrightarrow\sf\:\:Arithmetic\:Mean=\dfrac{415}{10}\\\\\\\dashrightarrow\:\: \underline{\boxed{\sf Arithmetic\:Mean = 41.5}}$

⠀

$\therefore\:\underline{\textsf{Arithmetic Mean of Distribution is \textbf{41.5}}.}$