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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 corresponds to Kris's description, we need to analyze the given options based on the mean, spread, and shape of the data.

  1. Mean: The mean is 2.
  2. Spread: The spread, possibly referring to the range, is 3.
  3. Shape: The overall shape of the set is skewed.

Let's examine each option against these criteria.

  1. First Option:

    • Counts: 0 circles above 1, 3 above 2, 3 above 3, 1 above 4, 1 above 5.
    • Data: 2, 3, 3, 4, 5 (from means).
    • Mean = (01 + 32 + 33 + 14 + 1*5)/8 = 2.25 (not 2).
    • Spread = maximum (5) - minimum (2) = 3 (correct).
    • Shape: It appears to be somewhat symmetric, so not skewed.

  2. Second Option:

    • Counts: 4 above 1, 2 above 2, 1 above 3, 0 above 4, 1 above 5.
    • Data: 1, 1, 1, 1, 2, 2, 3, 5 (from counts).
    • Mean = (41 + 22 + 13 + 04 + 1*5)/8 = 1.875 (not 2).
    • Spread = maximum (5) - minimum (1) = 4 (not 3).
    • Shape: This is skewed to the left.

  3. Third Option:

    • Counts: 1 above 1, 3 above 2, 4 above 3, 3 above 4, 1 above 5.
    • Data: Likely includes 1, 32, 43, 3*4, 5.
    • Mean = (11 + 32 + 43 + 34 + 1*5)/12 = (1 + 6 + 12 + 12 + 5)/12 = 36/12 = 3 (not 2).
    • Spread = maximum - minimum analysis cannot directly match.
    • Shape: Right skewed.

  4. Fourth Option:

    • Counts: 3 above 1, 3 above 2, 1 above 3, 1 above 4, 0 above 5.
    • Data: 1, 1, 1, 2, 2, 2, 3, 4.
    • Mean = (31 + 32 + 13 + 14 + 0*5)/8 = (3 + 6 + 3 + 4 + 0)/8 = 16/8 = 2 (correct).
    • Spread = maximum (4) - minimum (1) = 3 (correct).
    • Shape: It appears somewhat symmetrical and does not look skewed.

Based on this analysis, the option that corresponds to Kris's description is Fourth Option. However, since you described the shape as skewed, none of the options perfectly fits. Based on the options provided, the fourth option fits the mean and spread but not the skewness.

Please review these details for possible assumptions or additional context.