The mean of each dataset that follows is 10. Which dataset is more spread out? Justify your answer using the mean absolute deviation of each dataset. Round your answers to the nearest tenth.
Dataset #1: {5,8,9,10,12,12,14}
Dataset #2: {5,6,8,9,10,10,22}
To calculate the mean absolute deviation for each dataset, we need to find the absolute difference between each data point and the mean, then take the average of those differences.
For Dataset #1:
Mean absolute deviation = (|5-10| + |8-10| + |9-10| + |10-10| + |12-10| + |12-10| + |14-10|) / 7
Mean absolute deviation = (5 + 2 + 1 + 0 + 2 + 2 + 4) / 7
Mean absolute deviation = 1.9
For Dataset #2:
Mean absolute deviation = (|5-10| + |6-10| + |8-10| + |9-10| + |10-10| + |10-10| + |22-10|) / 7
Mean absolute deviation = (5 + 4 + 2 + 1 + 0 + 0 + 12) / 7
Mean absolute deviation = 4.3
Since the mean absolute deviation for Dataset #2 is larger than for Dataset #1, we can conclude that Dataset #2 is more spread out.