The mean absolute deviation of Dataset #1 is 48.2. Dataset #2 follows. Which dataset is more spread out?
Dataset #2: 401, 467, 489, 503, 568
(1 point)
To determine which dataset is more spread out, we need to compare the mean absolute deviation (MAD) of Dataset #2 to the MAD of Dataset #1.
Since the MAD of Dataset #1 is 48.2, we need to calculate the MAD of Dataset #2 using the formula:
MAD = Σ|xi - x̄| / n
where xi represents each data point in Dataset #2, x̄ is the mean of Dataset #2, and n is the number of data points in the dataset.
First, we calculate the mean of Dataset #2:
Mean = (401 + 467 + 489 + 503 + 568) / 5 = 484.4
Now, we calculate the MAD of Dataset #2:
MAD = (|401 - 484.4| + |467 - 484.4| + |489 - 484.4| + |503 - 484.4| + |568 - 484.4|) / 5
MAD = (83.4 + 17.4 + 4.6 + 18.6 + 83.6) / 5
MAD = 207.6 / 5
MAD = 41.52
Since the MAD of Dataset #2 is 41.52, which is smaller than the MAD of Dataset #1 (48.2), we can conclude that Dataset #2 is less spread out than Dataset #1.