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Question The following dataset is a list of the number of siblings for 10 children at a playground. Describe the spread of the dataset using the mean absolute deviation. Number of siblings = {0,0,1,1,1,1,1,2,3,5} (1 point) Responses The mean absolute deviation is 1.1. On average, the number of siblings each child has is about 1.1 siblings from the mean. The mean absolute deviation is 1.1. On average, the number of siblings each child has is about 1.1 siblings from the mean. The mean absolute deviation is 1.5. On average, the number of siblings each child has is about 1.5 siblings from the mean. The mean absolute deviation is 1.5. On average, the number of siblings each child has is about 1.5 siblings from the mean. The mean absolute deviation is 1.5. On average, the children at the playground have 1.5 siblings. The mean absolute deviation is 1.5. On average, the children at the playground have 1.5 siblings. The mean absolute deviation is 1.1. The number of siblings each child has is within 1.1 siblings from the mean. The mean absolute deviation is 1.1. The number of siblings each child has is within 1.1 siblings from the mean.

1 answer

To find the mean absolute deviation (MAD) for the given dataset of sibling counts, follow these steps:

  1. Calculate the mean of the dataset.
  2. Find the absolute deviations from the mean for each data point.
  3. Calculate the average of those absolute deviations.

Given dataset: {0, 0, 1, 1, 1, 1, 1, 2, 3, 5}

Step 1: Calculate the Mean

Mean = (Sum of all data points) / (Number of data points)

Sum = 0 + 0 + 1 + 1 + 1 + 1 + 1 + 2 + 3 + 5 = 15
Number of data points = 10

Mean = 15 / 10 = 1.5

Step 2: Calculate Absolute Deviations from the Mean

Now, find the absolute deviations from the mean for each data point:

  • |0 - 1.5| = 1.5
  • |0 - 1.5| = 1.5
  • |1 - 1.5| = 0.5
  • |1 - 1.5| = 0.5
  • |1 - 1.5| = 0.5
  • |1 - 1.5| = 0.5
  • |1 - 1.5| = 0.5
  • |2 - 1.5| = 0.5
  • |3 - 1.5| = 1.5
  • |5 - 1.5| = 3.5

Step 3: Calculate the Mean Absolute Deviation

Now, we'll average these absolute deviations:

Absolute Deviations = {1.5, 1.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1.5, 3.5}

Sum of Absolute Deviations = 1.5 + 1.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 1.5 + 3.5 = 10.0
Mean Absolute Deviation (MAD) = Sum of Absolute Deviations / Number of Data Points
MAD = 10.0 / 10 = 1.0

Conclusion

The mean absolute deviation is 1.0.

On average, the number of siblings each child has is about 1.0 siblings from the mean.

None of the provided options match this result, indicating there may have been an error in the provided calculations or responses.