calculate the average deviation from the mean for the following dataset
((14,15,16,17,18,19,20) round your answer to the nearest hundreth
the average deviation from the mean is what
To calculate the average deviation from the mean for the dataset (14, 15, 16, 17, 18, 19, 20), we first need to find the mean of the dataset:
Mean = (14 + 15 + 16 + 17 + 18 + 19 + 20) / 7
Mean = 119 / 7
Mean = 17
Next, we find the deviation of each data point from the mean:
Deviation from mean for 14: |14 - 17| = 3
Deviation from mean for 15: |15 - 17| = 2
Deviation from mean for 16: |16 - 17| = 1
Deviation from mean for 17: |17 - 17| = 0
Deviation from mean for 18: |18 - 17| = 1
Deviation from mean for 19: |19 - 17| = 2
Deviation from mean for 20: |20 - 17| = 3
Now, we calculate the sum of the absolute deviations:
Sum of deviations = 3 + 2 + 1 + 0 + 1 + 2 + 3
Sum of deviations = 12
Finally, we calculate the average deviation from the mean:
Average deviation from the mean = Sum of deviations / Number of data points
Average deviation from the mean = 12 / 7
Average deviation from the mean ≈ 1.71 (rounded to the nearest hundredth)
Therefore, the average deviation from the mean for the dataset (14, 15, 16, 17, 18, 19, 20) is approximately 1.71.