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Create a graphical representation of the following dataset representing the shoe sizes of a kindergarten class:

{10.5,11,10,10.5,11,10.5,11.5,10,9,9.5,10,10.5,10.5,10,11}

(1 point)
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An illustration shows a scatterplot. The x-axis is labeled shoe size and ranges from 9 to 13 in one unit increments. The y-axis is labeled student age and ranges from 0 to 8 in 2 unit increments. Points are plotted on the graph indicating values for each shoe size. The value for shoe size 9 is 5. The value for shoe size 9.5 is 5. The values for shoe size 10 are 5 and 6. The values for shoe size 10.5 are 5 and 6. The values for shoe size 11 are 5 and 6. The value for shoe size 11.5 is 6.
Image with alt text: An illustration shows a scatterplot. The x-axis is labeled shoe size and ranges from 9 to 13 in one unit increments. The y-axis is labeled student age and ranges from 0 to 8 in 2 unit increments. Points are plotted on the graph indicating values for each shoe size. The value for shoe size 9 is 5. The value for shoe size 9.5 is 5. The values for shoe size 10 are 5 and 6. The values for shoe size 10.5 are 5 and 6. The values for shoe size 11 are 5 and 6. The value for shoe size 11.5 is 6.

An illustration shows a bar graph. The x-axis is labeled shoe size and ranges from 9 to 11 and one half in half size increments. The y-axis is labeled frequency and ranges from 0 to 5 in one unit increments. The bar value for shoe size 9 is 1. The value for size 9.5 is 1. The value for size 10 is 4. The value for size 10.5 is 5. The value for size 11 is 3. The value for size 11.5 is 1.
Image with alt text: An illustration shows a bar graph. The x-axis is labeled shoe size and ranges from 9 to 11 and one half in half size increments. The y-axis is labeled frequency and ranges from 0 to 5 in one unit increments. The bar value for shoe size 9 is 1. The value for size 9.5 is 1. The value for size 10 is 4. The value for size 10.5 is 5. The value for size 11 is 3. The value for size 11.5 is 1.

An illustration shows a horizontal histogram. The x-axis is not labeled, but 5 vertical lines extend upward and parallel to the y-axis. The y-axis shows 3 value ranges. The value for the range of 9 to 9.5 extends to 4 vertical lines.The value for 10 to 10.5 extends to 5 vertical lines. The value for 11 to 11.5 extends to 2 vertical lines.
Image with alt text: An illustration shows a horizontal histogram. The x-axis is not labeled, but 5 vertical lines extend upward and parallel to the y-axis. The y-axis shows 3 value ranges. The value for the range of 9 to 9.5 extends to 4 vertical lines.The value for 10 to 10.5 extends to 5 vertical lines. The value for 11 to 11.5 extends to 2 vertical lines.

An illustration shows a line graph. The x-axis is labeled shoe size and ranges from 9 to 11 and one half in half size increments. The y-axis is labeled frequency and ranges from 0 to 5 in one unit increments. Points are plotted on the graph indicating values for each shoe size. A line connects the points. The value for shoe size 9 is 1. The value for size 9.5 is 1. The value for size 10 is 4. The value for size 10.5 is 5. The value for size 11 is 3. The value for size 11.5 is 1.
Image with alt text: An illustration shows a line graph. The x-axis is labeled shoe size and ranges from 9 to 11 and one half in half size increments. The y-axis is labeled frequency and ranges from 0 to 5 in one unit increments. Points are plotted on the graph indicating values for each shoe size. A line connects the points. The value for shoe size 9 is 1. The value for size 9.5 is 1. The value for size 10 is 4. The value for size 10.5 is 5. The value for size 11 is 3. The value for size 11.5 is 1.
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1 answer

To represent the dataset of shoe sizes of a kindergarten class effectively, the best choice among the options provided is the bar graph.

Reasoning:

  1. Bar Graph Representation:

    • It visually displays the frequency of each shoe size clearly.
    • Each bar represents a different shoe size, providing an immediate understanding of how many students have each size.

  2. Interpretation of Bar Graph Data:

    • The x-axis is labeled "shoe size" and ranges from 9 to 11.5 in half-size increments.
    • The y-axis is labeled "frequency" and ranges from 0 to 5 in one-unit increments.
    • The specific values are:
      • Shoe size 9: 1 student
      • Shoe size 9.5: 1 student
      • Shoe size 10: 4 students
      • Shoe size 10.5: 5 students
      • Shoe size 11: 3 students
      • Shoe size 11.5: 1 student

This representation allows for easy comparison of shoe sizes and gives a clear overview of the data.

The other formats, like scatterplots or line graphs, may not effectively convey the same information as the bar graph does with regard to frequency distribution in this context.

In summary, the bar graph best communicates the frequency distribution of shoe sizes within the kindergarten class, making it the most effective option.