To determine the Mean Absolute Deviation (MAD) for the dataset, we first need to calculate the mean of the likes:
Dataset: 17, 19, 21, 23, 28, 31, 31, 34, 35, 36
-
Calculate the Mean (Average): \[ \text{Mean} = \frac{(17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36)}{10} = \frac{ 17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36 }{10} \] \[ = \frac{ 28 + 36 + 70 + 31 + 32 }{10} = \frac{279}{10} = 27.9 \]
-
Calculate the Absolute Deviations from the Mean: \[ |17 - 27.9| = 10.9 \] \[ |19 - 27.9| = 8.9 \] \[ |21 - 27.9| = 6.9 \] \[ |23 - 27.9| = 4.9 \] \[ |28 - 27.9| = 0.1 \] \[ |31 - 27.9| = 3.1 \] \[ |31 - 27.9| = 3.1 \] \[ |34 - 27.9| = 6.1 \] \[ |35 - 27.9| = 7.1 \] \[ |36 - 27.9| = 8.1 \]
-
Calculate the Mean Absolute Deviation (MAD): \[ \text{MAD} = \frac{ (10.9 + 8.9 + 6.9 + 4.9 + 0.1 + 3.1 + 3.1 + 6.1 + 7.1 + 8.1) }{10} = \frac{ 59.1 }{10} = 5.91 \approx 6 \]
So the MAD is approximately 6.
Now we can conclude what this value means for the dataset.
Conclusion: The MAD is 6. This indicates that, on average, the number of likes Julia received on her posts deviates by approximately 6 likes from the mean of around 27.9 likes.
Thus, the correct response is: The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.