E. Which data points have an absolute deviation that is less than or equal to the MAD? These data points are said to be within the MAD. Choose all that apply. 104 92 107 83 96 98 91 90

Question

UpStudy AI · Accepted Answer

To determine which data points are within the Median Absolute Deviation (MAD), follow these steps:

1. **List the Data Points:**
   $$
   104, \, 92, \, 107, \, 83, \, 96, \, 98, \, 91, \, 90
   $$

2. **Calculate the Median:**
   - **Ordered Data:**
     $$
     83, \, 90, \, 91, \, 92, \, 96, \, 98, \, 104, \, 107
     $$
   - **Median Position:** Since there are 8 data points (even number), the median is the average of the 4th and 5th values.
     $$
     \text{Median} = \frac{92 + 96}{2} = 94
     $$

3. **Compute Absolute Deviations from the Median:**
   $$
   \begin{align*}
   |104 - 94| &= 10 \
   |92 - 94| &= 2 \
   |107 - 94| &= 13 \
   |83 - 94| &= 11 \
   |96 - 94| &= 2 \
   |98 - 94| &= 4 \
   |91 - 94| &= 3 \
   |90 - 94| &= 4 \
   \end{align*}
   $$
   - **Ordered Absolute Deviations:**
     $$
     2, \, 2, \, 3, \, 4, \, 4, \, 10, \, 11, \, 13
     $$

4. **Determine the MAD:**
   - **Median of Absolute Deviations:**
     $$
     \text{MAD} = \frac{4 + 4}{2} = 4
     $$

5. **Identify Data Points Within the MAD:**
   - **Criteria:** Absolute deviation ≤ MAD (4)
   - **Eligible Data Points:**
     $$
     90 \; (4), \; 91 \; (3), \; 92 \; (2), \; 96 \; (2), \; 98 \; (4)
     $$

**Final Answer:**
The data points within the MAD are **90, 91, 92, 96, and 98**.
The data points within the MAD are 90, 91, 92, 96, and 98.

E. Which data points have an absolute deviation that is less than or equal to the MAD? These data points are said to be within the MAD. Choose all that apply. 104 92 107 83 96 98 91 90

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions