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Construct a Pareto chart to represent the expenditure of a household with the following details: Food Rs. 800, Clothing Rs. 500, Education Rs. 400, Fuel Rs. 200, Misc. Rs. 100.

Business/Management

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Answer

To represent the data by a Pareto chart, we first need to calculate the percentage of expenditure for each item and then sort them in descending order. After that, we calculate the cumulative percentage.

Step-by-step solution

4 steps
  1. Calculate the total expenditure.

    Total expenditure =800+500+400+200+100=2000= 800 + 500 + 400 + 200 + 100 = 2000 Rs.

  2. Calculate the percentage of expenditure for each item.

    • Food: 8002000×100%=40%\frac{800}{2000} \times 100\% = 40\%
    • Clothing: 5002000×100%=25%\frac{500}{2000} \times 100\% = 25\%
    • Education: 4002000×100%=20%\frac{400}{2000} \times 100\% = 20\%
    • Fuel: 2002000×100%=10%\frac{200}{2000} \times 100\% = 10\%
    • Misc.: 1002000×100%=5%\frac{100}{2000} \times 100\% = 5\%
  3. Sort the items in descending order of expenditure and calculate the cumulative percentage.

    ItemExpenditure (Rs)Percentage (%)Cumulative Percentage (%)Food8004040Clothing5002540+25=65Education4002065+20=85Fuel2001085+10=95Misc.100595+5=100\begin{array}{|l|c|c|c|} \hline \textbf{Item} & \textbf{Expenditure (Rs)} & \textbf{Percentage (\%)} & \textbf{Cumulative Percentage (\%)} \\ \hline \text{Food} & 800 & 40 & 40 \\ \text{Clothing} & 500 & 25 & 40 + 25 = 65 \\ \text{Education} & 400 & 20 & 65 + 20 = 85 \\ \text{Fuel} & 200 & 10 & 85 + 10 = 95 \\ \text{Misc.} & 100 & 5 & 95 + 5 = 100 \\ \hline \end{array}
  4. Construct the Pareto chart.

    A Pareto chart is a bar chart where the bars are arranged in descending order of frequency or cost, combined with a line graph that shows the cumulative percentage.

    • The x-axis would list the items in the order: Food, Clothing, Education, Fuel, Misc.
    • The left y-axis would represent the expenditure in Rupees, ranging from 0 to 800. Bars would be drawn for each item corresponding to its expenditure.
    • The right y-axis would represent the cumulative percentage, ranging from 0% to 100%. A line graph would be plotted using the cumulative percentages for each item.

    The table above provides all the necessary data to construct the Pareto chart.

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