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Calculate the average deviation from the mean for the following dataset: {23,24,26,27,28,30,31}
{
23
,
24
,
26
,
27
,
28
,
30
,
31
}
. Round your answer to the nearest hundredth.(1 point)
The average deviation from the mean is BLANK.

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 Absolute 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

    Therefore, the absolute deviations are: {4, 3, 1, 0, 1, 3, 4}.

  3. Calculate the Average Deviation: \[ \text{Average Deviation} = \frac{4 + 3 + 1 + 0 + 1 + 3 + 4}{7} = \frac{16}{7} \approx 2.2857 \]

  4. Round to the Nearest Hundredth: \[ \text{Average Deviation} \approx 2.29 \]

Thus, the average deviation from the mean is 2.29.