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Calculate the average deviation from the mean for the following dataset: {23,24,26,27,28,30,31}

. Round your answer to the nearest hundredth.(1 point)
The average deviation from the mean is (give a solid number)

1 answer

To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, follow these steps:

  1. Calculate the mean: \[ \text{Mean} = \frac{23 + 24 + 26 + 27 + 28 + 30 + 31}{7} = \frac{189}{7} = 27 \]

  2. Calculate the deviations from the mean: \[ |23 - 27| = 4 \] \[ |24 - 27| = 3 \] \[ |26 - 27| = 1 \] \[ |27 - 27| = 0 \] \[ |28 - 27| = 1 \] \[ |30 - 27| = 3 \] \[ |31 - 27| = 4 \]

  3. Calculate the sum of the absolute deviations: \[ 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16 \]

  4. Calculate the average deviation: \[ \text{Average Deviation} = \frac{16}{7} \approx 2.285714285714286 \]

  5. Round to the nearest hundredth: \[ \text{Average Deviation} \approx 2.29 \]

Thus, the average deviation from the mean is 2.29.