(i) A factory has five sections employing 105,184,130,93 and...

(i) A factory has five sections employing $105,184,130,93$ and 125 workers. The mean earnings in a certain week per worker are Rs $13.80$, Rs $15.00$, Rs $15.20$, Rs $18.20$ and Rs $14.20$ for the 5 sections. Determine the mean earning per worker of the whole factory. [Dip. Management, '70] (ii) In a survey of locality the following figures regarding the income of the people in different occupations were received. Find out the average per capita income: $$ \begin{array}{|l|c|c|} \hline \text { Occupation } & \begin{array}{c} \text { Average Income } \\ (\text { in } R s) \end{array} & \text { \mathrm{Number of People } } \\ \hline \text { Business } & 500 & 700 \\ \text { Labour } & 300 & 300 \\ \text { Craftmanship } & 200 & 200 \\ \text { Other } & 400 & 100 \\ \hline \end{array} $$

(i) A factory has five sections employing $105,184,130,93$ and 125 workers. The mean earnings in a certain week per worker are Rs $13.80$, Rs $15.00$, Rs $15.20$, Rs $18.20$ and Rs $14.20$ for the 5 sections. Determine the mean earning per worker of the whole factory. [Dip. Management, '70]
(ii) In a survey of locality the following figures regarding the income of the people in different occupations were received. Find out the average per capita income:
$$
\begin{array}{|l|c|c|}
\hline \text { Occupation } & \begin{array}{c}
\text { Average Income } \\
(\text { in } R s)
\end{array} & \text { \mathrm{Number of People } } \\
\hline \text { Business } & 500 & 700 \\
\text { Labour } & 300 & 300 \\
\text { Craftmanship } & 200 & 200 \\
\text { Other } & 400 & 100 \\
\hline
\end{array}
$$

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Key Concepts

Frequency Distribution

Frequency distribution refers to the way data points are distributed among various categories or groups, indicating how many observations fall into each category. Understanding the frequency distribution is crucial when applying the weighted mean, as it provides the weights that adjust the impact of each group on the overall average.

Weighted Arithmetic Mean

The weighted arithmetic mean is a method of calculating an average when different data points contribute unequally to the total. It is computed by multiplying each value by its corresponding weight (or frequency), summing these products, and then dividing by the sum of the weights. This method ensures that groups with more elements have a larger impact on the overall average.

Data Aggregation

Data aggregation involves consolidating multiple sets of data into a single, comprehensive value. In the context of computing averages, this means summing all weighted values and then dividing by the total number of elements. This process is essential when synthesizing information from various categories or groups to determine an overall statistic.

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