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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: 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: 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.
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1 answer

To solve this problem, we need to assess each dataset based on the summary provided by Kris:

  1. Mean of 2: This means that the average of the values in the dataset must be 2.
  2. Spread of 3: This likely refers to the range of the dataset, which means the difference between the highest and lowest values should be 3.
  3. Shape is skewed: This suggests that the data distribution is not symmetrical; it either has a longer tail on one side (skewed right or left).

Now, let's analyze each option provided:

  1. First option:

    • Values: 2 (3 times), 3 (3 times), 4 (1 time), 5 (1 time)
    • Calculation of the mean: (23 + 33 + 41 + 51)/8 = (6 + 9 + 4 + 5)/8 = 24/8 = 3 (not 2)
    • Not a match.

  2. Second option:

    • Values: 1 (1 time), 2 (3 times), 3 (4 times), 4 (3 times), 5 (1 time)
    • Mean Calculation: (11 + 23 + 34 + 43 + 5*1)/12 = (1 + 6 + 12 + 12 + 5)/12 = 36/12 = 3 (not 2)
    • Not a match.

  3. Third option:

    • Values: 1 (4 times), 2 (2 times), 3 (1 time), 5 (1 time)
    • Mean Calculation: (14 + 22 + 31 + 00 + 5*1)/8 = (4 + 4 + 3 + 0 + 5)/8 = 16/8 = 2 (Correct)
    • Range: 5 - 1 = 4 (not 3)
    • While it has the correct mean, the range does not match.
    • Not a match.

  4. Fourth option:

    • Values: 1 (3 times), 2 (3 times), 3 (1 time), 4 (1 time)
    • Mean Calculation: (13 + 23 + 31 + 41)/8 = (3 + 6 + 3 + 4)/8 = 16/8 = 2 (Correct)
    • Range: 4 - 1 = 3 (Correct)
    • The skew comes from the greater number of lower values (3 ones and 3 twos compared to 1 three and 1 four).
    • This distribution is indeed skewed.

From the evaluations, the fourth option is the only one that meets all three conditions set by Kris.

Thus, the correct answer is the fourth option.