Final answer:
To calculate the mean absolute deviation of the data set {5,8,8,10,13,14,16,22}, first find the mean, then calculate each point's absolute deviation from the mean, and finally find the mean of those deviations. The mean absolute deviation is 4.25.
Step-by-step explanation:
Calculating the Mean Absolute Deviation
To calculate the mean absolute deviation (MAD) of the data set 5, 8, 8, 10, 13, 14, 16, 22, you must follow several steps. First, find the mean (average) of the data set. Add all the numbers and divide by the total count of numbers. The mean is (5+8+8+10+13+14+16+22)/8 = 96/8 = 12. Next, find the absolute deviation of each data point from the mean, which is the absolute value of the difference between each data point and the mean. Then find the mean of those absolute deviations to get the MAD:
- Absolute deviation for 5: |5 - 12| = 7
- Absolute deviation for 8: |8 - 12| = 4 (This occurs twice since 8 is repeated)
- Absolute deviation for 10: |10 - 12| = 2
- Absolute deviation for 13: |13 - 12| = 1
- Absolute deviation for 14: |14 - 12| = 2
- Absolute deviation for 16: |16 - 12| = 4
- Absolute deviation for 22: |22 - 12| = 10
Sum of absolute deviations = 7 + 4 + 4 + 2 + 1 + 2 + 4 + 10 = 34
Finally, divide the sum of the absolute deviations by the number of data points: MAD = 34/8 = 4.25.
The mean absolute deviation of this data set is 4.25.