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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}
{
0
,
0
,
1
,
1
,
1
,
1
,
1
,
2
,
3
,
5
}

(1 point)
Responses

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.

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 1.1. 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.

1 answer

To calculate the mean absolute deviation (MAD) of the dataset, we first need to find the mean of the data.

Step 1: Calculate the Mean

The dataset is: {0, 0, 1, 1, 1, 1, 1, 2, 3, 5}

  1. Sum of the values: \[ 0 + 0 + 1 + 1 + 1 + 1 + 1 + 2 + 3 + 5 = 14 \]

  2. Count of the values: There are 10 children, so the count is 10.

  3. Mean: \[ \text{Mean} = \frac{\text{Sum of values}}{\text{Count}} = \frac{14}{10} = 1.4 \]

Step 2: Calculate the Absolute Deviations

Next, we find the absolute deviations from the mean for each value:

  • \(|0 - 1.4| = 1.4\)
  • \(|0 - 1.4| = 1.4\)
  • \(|1 - 1.4| = 0.4\)
  • \(|1 - 1.4| = 0.4\)
  • \(|1 - 1.4| = 0.4\)
  • \(|1 - 1.4| = 0.4\)
  • \(|1 - 1.4| = 0.4\)
  • \(|2 - 1.4| = 0.6\)
  • \(|3 - 1.4| = 1.6\)
  • \(|5 - 1.4| = 3.6\)

Step 3: Calculate the Mean Absolute Deviation

Now, we sum these absolute deviations: \[ 1.4 + 1.4 + 0.4 + 0.4 + 0.4 + 0.4 + 0.4 + 0.6 + 1.6 + 3.6 = 10.2 \]

Now, we divide this sum by the number of values (10) to find the mean absolute deviation: \[ \text{MAD} = \frac{10.2}{10} = 1.02 \]

Conclusion

The calculated mean absolute deviation is approximately \(1.02\). Since none of the provided choices exactly match this result, it is closest to:

The mean absolute deviation is 1.1. On average, the number of siblings each child has is about 1.1 siblings from the mean.

Thus, the best choice according to rounding is:

The mean absolute deviation is 1.1. On average, the children at the playground have about 1.1 siblings from the mean.