To find the mean absolute deviation (MAD) of the dataset, we can follow these steps:
- Calculate the mean (average) of the dataset.
- Calculate the absolute deviations from the mean for each data point.
- Calculate the mean of these absolute deviations.
Step 1: Calculate the Mean
First, let's sum the dataset:
\[ 141 + 156 + 204 + 218 + 118 + 151 + 181 = 1069 \]
Now we divide by the number of data points (which is 7):
\[ \text{Mean} = \frac{1069}{7} \approx 152.7142857 \]
Rounding this to one decimal place, we get:
\[ \text{Mean} \approx 152.7 \]
Step 2: Calculate Absolute Deviations from the Mean
Now, we will find the absolute deviation of each point from the mean \( 152.7 \):
- \( |141 - 152.7| = | -11.7| = 11.7 \)
- \( |156 - 152.7| = |3.3| = 3.3 \)
- \( |204 - 152.7| = |51.3| = 51.3 \)
- \( |218 - 152.7| = |65.3| = 65.3 \)
- \( |118 - 152.7| = | -34.7| = 34.7 \)
- \( |151 - 152.7| = | -1.7| = 1.7 \)
- \( |181 - 152.7| = |28.3| = 28.3 \)
Step 3: Calculate the Mean of Absolute Deviations
Now we sum up the absolute deviations:
\[ 11.7 + 3.3 + 51.3 + 65.3 + 34.7 + 1.7 + 28.3 = 196.3 \]
Now divide by the number of data points (7):
\[ \text{MAD} = \frac{196.3}{7} \approx 28.04 \]
Rounding to the nearest tenth, we get:
\[ \text{MAD} \approx 28.0 \]
Therefore, the mean absolute deviation of the dataset is 28.0.