Question

Question
Dataset A, {7,9,9,12}
, and dataset B, {6,8,10,13}
, both have a mean of 9.25. Calculate the average deviation from the mean of each dataset.(1 point)
The average deviation from the mean of dataset A is
. The average deviation from the mean of dataset B is
.

Answer 1

To calculate the average deviation from the mean for each dataset, follow these steps:

1. **Calculate the deviations from the mean for each data point in the dataset**.
2. **Take the absolute value of each deviation**.
3. **Calculate the mean of these absolute deviations** (this is the average deviation from the mean).

### Dataset A: {7, 9, 9, 12}

- Mean = 9.25
- Deviations from the mean:
- |7 - 9.25| = | -2.25| = 2.25
- |9 - 9.25| = | -0.25| = 0.25
- |9 - 9.25| = | -0.25| = 0.25
- |12 - 9.25| = |2.75| = 2.75

- Absolute deviations: {2.25, 0.25, 0.25, 2.75}

- Average deviation for Dataset A:
\[
\text{Average Deviation} = \frac{2.25 + 0.25 + 0.25 + 2.75}{4} = \frac{5.5}{4} = 1.375
\]

### Dataset B: {6, 8, 10, 13}

- Mean = 9.25
- Deviations from the mean:
- |6 - 9.25| = | -3.25| = 3.25
- |8 - 9.25| = | -1.25| = 1.25
- |10 - 9.25| = |0.75| = 0.75
- |13 - 9.25| = |3.75| = 3.75

- Absolute deviations: {3.25, 1.25, 0.75, 3.75}

- Average deviation for Dataset B:
\[
\text{Average Deviation} = \frac{3.25 + 1.25 + 0.75 + 3.75}{4} = \frac{9.0}{4} = 2.25
\]

### Final Results
- The average deviation from the mean of dataset A is **1.375**.
- The average deviation from the mean of dataset B is **2.25**.