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Complete the cumulative frequency table for the data.

Mathematics

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Answer

To complete the cumulative frequency table, we read the coordinates of the points on the ogive. The x-axis represents the percentage of income (upper class boundary), and the y-axis represents the cumulative frequency.

Step-by-step solution

2 steps
  1. Identify the coordinates of the points on the ogive.

    • At x=20x = 20, the cumulative frequency is y=0y = 0.
    • At x=30x = 30, the cumulative frequency is y=10y = 10.
    • At x=40x = 40, the cumulative frequency is y=25y = 25.
    • At x=50x = 50, the cumulative frequency is y=45y = 45.
    • At x=60x = 60, the cumulative frequency is y=55y = 55.
    • At x=70x = 70, the cumulative frequency is y=60y = 60.
  2. Construct the cumulative frequency table using these points.

    The "Percentage of Income" column will represent the upper class boundaries, and the "Cumulative Frequency" column will show the corresponding cumulative frequencies.

    Percentage of IncomeCumulative Frequencyx≤200x≤3010x≤4025x≤5045x≤6055x≤7060\begin{array}{|c|c|} \hline \textbf{Percentage of Income} & \textbf{Cumulative Frequency} \\ \hline x \le 20 & 0 \\ \hline x \le 30 & 10 \\ \hline x \le 40 & 25 \\ \hline x \le 50 & 45 \\ \hline x \le 60 & 55 \\ \hline x \le 70 & 60 \\ \hline \end{array}

    The completed cumulative frequency table is shown above.

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