Question

The dataset represents the number of likes Julia had on her last 10 Instagram posts:

17, 19, 21, 23, 28, 31, 31, 34, 35, 36
Which of the following is the MAD of the dataset and explains what the value means for this dataset?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the MAD (Mean Absolute Deviation) of the dataset, we first need to find the mean of the data:

Mean = (17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36) / 10
Mean = 275 / 10
Mean = 27.5

Next, we find the absolute deviation of each data point from the mean:

|17 - 27.5| = 10.5
|19 - 27.5| = 8.5
|21 - 27.5| = 6.5
|23 - 27.5| = 4.5
|28 - 27.5| = 0.5
|31 - 27.5| = 3.5
|31 - 27.5| = 3.5
|34 - 27.5| = 6.5
|35 - 27.5| = 7.5
|36 - 27.5| = 8.5

Now, we calculate the MAD by finding the mean of these absolute deviations:

MAD = (10.5 + 8.5 + 6.5 + 4.5 + 0.5 + 3.5 + 3.5 + 6.5 + 7.5 + 8.5) / 10
MAD = 59 / 10
MAD = 5.9

Therefore, the MAD of the dataset is 5.9. The MAD measures the average absolute distance between each data point and the mean of the dataset. In this case, a MAD of 5.9 means that, on average, each data point is about 5.9 likes away from the mean of 27.5 likes. This value provides an indication of the variability or dispersion of the data points around the mean.