To calculate the Mean Absolute Deviation (MAD) of the dataset, we first need to find the mean of the dataset:
Mean = (17 + 19 + 21 + 23 + 28 + 31 + 31 + 34 + 35 + 36) / 10
Mean = 275 / 10
Mean = 27.5
Next, we calculate the absolute deviations of each data point from the mean and then find the average of those absolute deviations to get the MAD:
|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
Average Absolute Deviation = (10.5 + 8.5 + 6.5 + 4.5 + 0.5 + 3.5 + 3.5 + 6.5 + 7.5 + 8.5) / 10
Average Absolute Deviation = 59.5 / 10
Average Absolute Deviation = 5.95
Therefore, the Mean Absolute Deviation (MAD) of the dataset is 5.95.
The MAD gives us a measure of how spread out the data points are from the mean. In this case, the MAD value of 5.95 indicates that on average, the number of likes Julia received on her Instagram posts deviates from the mean of 27.5 by approximately 5.95 likes. This can help us understand the variability in the number of likes Julia receives on her posts.
This 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?
1 answer