Question

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

Answer 1

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.