Question
A set of data has the values 34, 40, 42, 48, and 70. If the outlier of 70 is removed, what is the mean absolute deviation of the remaining four values?
3.2
4
11.2
14
3.2
4
11.2
14
Answers
GPT-4o mini
To calculate the mean absolute deviation (MAD) of the remaining values after removing the outlier 70, follow these steps:
1. **Remove the outlier**: The remaining values are 34, 40, 42, and 48.
2. **Calculate the mean** of the remaining values:
\[
\text{Mean} = \frac{34 + 40 + 42 + 48}{4} = \frac{164}{4} = 41
\]
3. **Calculate the absolute deviations** of each value from the mean:
- For 34: \( |34 - 41| = 7 \)
- For 40: \( |40 - 41| = 1 \)
- For 42: \( |42 - 41| = 1 \)
- For 48: \( |48 - 41| = 7 \)
4. **Calculate the mean of these absolute deviations**:
\[
\text{Mean Absolute Deviation} = \frac{7 + 1 + 1 + 7}{4} = \frac{16}{4} = 4
\]
Thus, the mean absolute deviation of the remaining values is **4**.
1. **Remove the outlier**: The remaining values are 34, 40, 42, and 48.
2. **Calculate the mean** of the remaining values:
\[
\text{Mean} = \frac{34 + 40 + 42 + 48}{4} = \frac{164}{4} = 41
\]
3. **Calculate the absolute deviations** of each value from the mean:
- For 34: \( |34 - 41| = 7 \)
- For 40: \( |40 - 41| = 1 \)
- For 42: \( |42 - 41| = 1 \)
- For 48: \( |48 - 41| = 7 \)
4. **Calculate the mean of these absolute deviations**:
\[
\text{Mean Absolute Deviation} = \frac{7 + 1 + 1 + 7}{4} = \frac{16}{4} = 4
\]
Thus, the mean absolute deviation of the remaining values is **4**.