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Kris writes the following description of a dataset:

The mean of the set is 2.
The spread of the set is 3.
The overall shape of the set is skewed.

Which of these is Kris’s dataset?

(1 point)
Responses

An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 1 circle above 1, 3 circles above 2, 4 circles above 3, 3 circles above 4, and 1 circle above 5.
Image with alt text: An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 1 circle above 1, 3 circles above 2, 4 circles above 3, 3 circles above 4, and 1 circle above 5.

An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 0 circles above 1, 3 circles above 2, 3 circles above 3, 1 circle above 4, and 1 circle above 5.
Image with alt text: An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 0 circles above 1, 3 circles above 2, 3 circles above 3, 1 circle above 4, and 1 circle above 5.

An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 4 circles above 1, 2 circles above 2, 1 circle above 3, 0 circles above 4, and 1 circle above 5.
Image with alt text: An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertically above each number in the number line. The number of circles above each number in the number line are as follows: 4 circles above 1, 2 circles above 2, 1 circle above 3, 0 circles above 4, and 1 circle above 5.

An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertially above each number in the number line. The number of circles above each number in the number line are as follows: 3 circles above 1, 3 circles above 2, 1 circle above 3, 1 circle above 4, and 0 circles above 5.
Image with alt text: An illustration shows a number line ranging from 1 to 5 in unit increments. Different numbers of open circles are placed vertially above each number in the number line. The number of circles above each number in the number line are as follows: 3 circles above 1, 3 circles above 2, 1 circle above 3, 1 circle above 4, and 0 circles above 5.

1 answer

To determine which dataset matches Kris's description, we need to analyze the characteristics given:

  1. The mean of the set is 2.
  2. The spread (presumably the range) of the set is 3.
  3. The overall shape of the set is skewed.

Now let's evaluate each of the provided datasets based on these criteria:

  1. First option:

    • Circles above: 1 (1), 3 (2), 4 (3), 3 (4), 1 (5)
    • Data: {1, 2, 2, 3, 3, 3, 4, 4, 5}
    • Mean: (1 + 23 + 34 + 4 + 5) / 11 = 2.36 (not 2)
    • Spread: 5 - 1 = 4 (not 3)
    • Shape: Slightly skewed right due to more 3s and 4s.

  2. Second option:

    • Circles above: 0 (1), 3 (2), 3 (3), 1 (4), 1 (5)
    • Data: {2, 2, 2, 3, 4, 5}
    • Mean: (2*3 + 3 + 4 + 5) / 6 = 3.33 (not 2)
    • Spread: 5 - 2 = 3 (correct but mean is wrong)
    • Shape: Symmetric.

  3. Third option:

    • Circles above: 4 (1), 2 (2), 1 (3), 0 (4), 1 (5)
    • Data: {1, 1, 1, 1, 2, 2, 3, 5}
    • Mean: (14 + 22 + 3 + 5) / 8 = 2.25 (not 2)
    • Spread: 5 - 1 = 4 (not 3)
    • Shape: Skewed left due to more 1s.

  4. Fourth option:

    • Circles above: 3 (1), 3 (2), 1 (3), 1 (4), 0 (5)
    • Data: {1, 1, 1, 2, 2, 3, 4}
    • Mean: (13 + 22 + 3 + 4) / 7 = 2 (correct)
    • Spread: 4 - 1 = 3 (correct)
    • Shape: Skewed right as more lower values exist (1s).

The dataset that matches Kris's description is the fourth option.