Question

A) 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. The average deviation from the mean of each dataset. A is B is

Answer 1

To calculate the average deviation from the mean for both datasets, we need to follow these steps:

1. Find the mean (which is already given in this case).
2. Calculate the absolute deviations from the mean for each value in the dataset.
3. Find the average of these absolute deviations.

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

1. Mean \( = 9.25 \)
2. Absolute deviations from the mean:
- \( |7 - 9.25| = | -2.25| = 2.25 \)
- \( |9 - 9.25| = | -0.25| = 0.25 \)
- \( |9 - 9.25| = | -0.25| = 0.25 \)
- \( |12 - 9.25| = |2.75| = 2.75 \)

3. Average deviation:
\[
\text{Average Deviation} = \frac{(2.25 + 0.25 + 0.25 + 2.75)}{4} = \frac{5.5}{4} = 1.375
\]

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

1. Mean \( = 9.25 \)
2. Absolute deviations from the mean:
- \( |6 - 9.25| = |-3.25| = 3.25 \)
- \( |8 - 9.25| = |-1.25| = 1.25 \)
- \( |10 - 9.25| = |0.75| = 0.75 \)
- \( |13 - 9.25| = |3.75| = 3.75 \)

3. Average deviation:
\[
\text{Average Deviation} = \frac{(3.25 + 1.25 + 0.75 + 3.75)}{4} = \frac{9}{4} = 2.25
\]

**Final Results:**
- Average deviation for Dataset A is **1.375**.
- Average deviation for Dataset B is **2.25**.