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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: 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 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 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.
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1 answer

To determine which dataset matches Kris's description, let's analyze the given information:

  1. Mean = 2: This means that the average of the numbers in the dataset must equal 2.

  2. Spread = 3: The spread refers to the range of the dataset, which is calculated as the difference between the maximum and minimum values. Here, if we assume the spread is 3, then if the minimum value is \(x\), the maximum value must be \(x + 3\).

  3. Skewed Shape: The dataset is not symmetrical and has a longer tail on one side.

Let's evaluate each of the provided datasets to see which one meets these criteria:

  1. Dataset with circles above:

    • 0 at 1
    • 3 at 2
    • 3 at 3
    • 1 at 4
    • 1 at 5
    • Mean = (01 + 32 + 33 + 14 + 1*5) / (0 + 3 + 3 + 1 + 1) = (0 + 6 + 9 + 4 + 5) / 8 = 24 / 8 = 3 → does not match mean.
    • Spread = 5 - 1 = 4 → does not match spread.

  2. Dataset with circles above:

    • 4 at 1
    • 2 at 2
    • 1 at 3
    • 0 at 4
    • 1 at 5
    • Mean = (41 + 22 + 13 + 04 + 1*5) / (4 + 2 + 1 + 0 + 1) = (4 + 4 + 3 + 0 + 5) / 8 = 16 / 8 = 2 → matches mean.
    • Spread = 5 - 1 = 4 → does not match spread.

  3. Dataset with circles above:

    • 1 at 1
    • 3 at 2
    • 4 at 3
    • 3 at 4
    • 1 at 5
    • Mean = (11 + 32 + 43 + 34 + 1*5) / (1 + 3 + 4 + 3 + 1) = (1 + 6 + 12 + 12 + 5) / 12 = 36 / 12 = 3 → does not match mean.
    • Spread = 5 - 1 = 4 → does not match spread.

  4. Dataset with circles above:

    • 3 at 1
    • 3 at 2
    • 1 at 3
    • 1 at 4
    • 0 at 5
    • Mean = (31 + 32 + 13 + 14 + 0*5) / (3 + 3 + 1 + 1 + 0) = (3 + 6 + 3 + 4 + 0) / 8 = 16 / 8 = 2 → matches mean.
    • Spread = 5 - 1 = 4 → does not match spread.

None of the datasets match the required spread of 3 and mean of 2, while some have matching means but incorrect spread or vice versa.

Based on the available options, the correct dataset with a mean of 2 is the second or fourth data set, but since they do not comply with the spread criteria, the answer remains ambiguous given that it might be a conflicting interpretation of expected values.

If you need a recommendation strictly based on systematically assessing compliance with description, the second dataset meets mean criteria squarely, albeit lacking with spread interpretation, please mark it if further inquiries are specified.