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What do you think of when you hear the word statistics?

Mathematics

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Step-by-step solution

5 steps

Part 1

When I hear the word statistics, I think of the practice of collecting, analyzing, interpreting, presenting, and organizing data. It's about using numerical data to find patterns, make predictions, and draw conclusions about a larger group or phenomenon.

Part 2· 5 steps

To illustrate the table as a Pie Chart, we first need to complete the data for all products. From the given information, we have:

  • Product 1: 9 customers, Relative Frequency = 930\frac{9}{30}. This means the total number of customers is 30.
  • Product 2: 13 customers.
  • The remaining customers for Product 3 = Total customers - (Product 1 customers + Product 2 customers) = 30−(9+13)=30−22=830 - (9 + 13) = 30 - 22 = 8 customers.

Now, we calculate the relative frequency, percentage, and the angle for each product in the pie chart.

  1. Calculate the relative frequency, percentage, and angle for Product 1.

    Number of Customers = 9
    Relative Frequency = 930\frac{9}{30}
    Percentage = 930×100%=30%\frac{9}{30} \times 100\% = 30\%
    Angle for Pie Chart = 930×360∘=108∘\frac{9}{30} \times 360^\circ = 108^\circ

  2. Calculate the relative frequency, percentage, and angle for Product 2.

    Number of Customers = 13
    Relative Frequency = 1330\frac{13}{30}
    Percentage = 1330×100%≈43.33%\frac{13}{30} \times 100\% \approx 43.33\%
    Angle for Pie Chart = 1330×360∘=156∘\frac{13}{30} \times 360^\circ = 156^\circ

  3. Calculate the relative frequency, percentage, and angle for Product 3.

    Number of Customers = 8
    Relative Frequency = 830\frac{8}{30}
    Percentage = 830×100%≈26.67%\frac{8}{30} \times 100\% \approx 26.67\%
    Angle for Pie Chart = 830×360∘=96∘\frac{8}{30} \times 360^\circ = 96^\circ

  4. Summarize the data for the pie chart.

    • Product 1 (9 customers): 30%30\% of the pie, corresponding to an angle of 108∘108^\circ.
    • Product 2 (13 customers): 43.33%43.33\% of the pie, corresponding to an angle of 156∘156^\circ.
    • Product 3 (8 customers): 26.67%26.67\% of the pie, corresponding to an angle of 96∘96^\circ.
  5. Instructions for drawing the Pie Chart.

    1. Draw a circle using a compass.
    2. Mark the center of the circle.
    3. Draw a radius from the center to the circumference. This will be your starting line.
    4. Using a protractor, measure and draw the first angle (108∘108^\circ for Product 1) from the starting line. Draw another radius to mark the end of this sector.
    5. From the new radius, measure and draw the second angle (156∘156^\circ for Product 2). Draw a third radius.
    6. The remaining sector will automatically represent the third angle (96∘96^\circ for Product 3).
    7. Label each sector with the product name and its corresponding percentage. You can also use different colors for each sector.

    Here is the completed table with the calculated values:

    \begin{array}{|l|c|c|c|} \hline \textbf{Product} & \textbf{Number of Customers} & \textbf{Relative Frequency} & \textbf{Percentage} & \textbf{Angle for Pie Chart} \\ \hline \text{Product 1} & 9 & \frac{9}{30} & 30\% & 108^\circ \\ \text{Product 2} & 13 & \frac{13}{30} & 43.33\% & 156^\circ \\ \text{Product 3} & 8 & \frac{8}{30} & 26.67\% & 96^\circ \\ \hline \textbf{Total} & \textbf{30} & \textbf{1} & \textbf{100\%} & \textbf{360^\circ} \\ \hline \end{array}

    The pie chart would be drawn using these angles.

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