Question

The number of apples produced per tree in Rabinsky’s orchard is: 

141, 156, 204, 218, 118, 151, 181



What is the mean absolute deviation of the dataset? Round to the nearest tenth.

Answer 1

To find the mean absolute deviation (MAD) of the dataset, we can follow these steps:

1. **Calculate the mean (average) of the dataset.**
2. **Calculate the absolute deviations from the mean for each data point.**
3. **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**.