Question

Incomplete information obtained from a partially destroyed records on cost of living analysis is given below: $$ \begin{array}{l|c|c} \hline \text { Group } & \text { Group Index } & \text { Percent }(\%) \text { of Total Expenditure } \\ \hline \text { Food } & 268 & 60 \\ \text { Clothing } & 280 & \text { Not available } \\ \text { Housing } & 210 & 50 \\ \text { Fuel and Electricity } & 240 & 5 \\ \text { Miscellaneous } & 260 & \text { Not available } \\ \hline \end{array} $$

   Incomplete information obtained from a partially destroyed records on cost of living analysis is given below:
$$
\begin{array}{l|c|c}
\hline \text { Group } & \text { Group Index } & \text { Percent }(\%) \text { of Total Expenditure } \\
\hline \text { Food } & 268 & 60 \\
\text { Clothing } & 280 & \text { Not available } \\
\text { Housing } & 210 & 50 \\
\text { Fuel and Electricity } & 240 & 5 \\
\text { Miscellaneous } & 260 & \text { Not available } \\
\hline
\end{array}
$$
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BUSINESS STATISTICS
BUSINESS STATISTICS
S. C. Gupta and… 2nd Edition
Chapter 10, Problem 16 ↓

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The table provided has missing data for the percentage of total expenditure for the "Clothing" and "Miscellaneous" groups.  Show more…

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Incomplete information obtained from a partially destroyed records on cost of living analysis is given below: $$ \begin{array}{l|c|c} \hline \text { Group } & \text { Group Index } & \text { Percent }(\%) \text { of Total Expenditure } \\ \hline \text { Food } & 268 & 60 \\ \text { Clothing } & 280 & \text { Not available } \\ \text { Housing } & 210 & 50 \\ \text { Fuel and Electricity } & 240 & 5 \\ \text { Miscellaneous } & 260 & \text { Not available } \\ \hline \end{array} $$
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Key Concepts

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Data Imputation and Reconstruction
Data imputation and reconstruction refer to the methods used for estimating missing values within a dataset. When certain key pieces of information are incomplete or lost, these techniques enable analysts to reconstruct a consistent data framework, ensuring behind-the-scenes calculations remain accurate and reliable for comprehensive analysis.
Weighting in Composite Indices
Weighting in composite indices assigns relative importance to different components based on their expenditure share or relevance in the overall calculation. In the context of cost of living, weights represent the percentage of total expenditure allocated to each category, ensuring that the impact of each category on the final index reflects its economic significance.
Cost of Living Analysis
Cost of living analysis involves assessing the overall changes in the prices of goods and services that households buy, reflecting how affordable it is for consumers to maintain their standard of living over time. It encompasses various categories such as food, housing, and transportation, and is critical for economic planning and policy formulation.
Index Numbers
Index numbers are statistical measures used to compare the relative change in economic variables, such as prices, over time. They help in quantifying changes in the cost of living or other economic aggregations by providing a baseline for measurement, thereby facilitating comparisons across different time periods.

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From the table of group index numbers and group expenditures given below calculate the cost of living index number: $$ \begin{array}{|l|c|c|} \hline \text { Group } & \text { Index Number } & \begin{array}{c} \text { Percentage of } \\ \text { Total Expenditure } \end{array} \\ \hline \text { Food } & 428 & 45 \\ \text { Clothing } & 250 & 15 \\ \text { Fuel and light } & 220 & 8 \\ \text { House rent } & 125 & 20 \\ \text { Others } & 175 & 12 \\ \hline \end{array} $$

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