Question

Helen recorded the number of tomatoes on each of her tomato plants and then arranged the numbers from smallest to largest.

The number of tomatoes on each plant were 5, 5, 5, 6, 9, 10, 10,10, 10, and 10. The mean number of tomatoes was 8.

What is the mean absolute deviation?

Answer 1

To calculate the mean absolute deviation (MAD), follow these steps:

1. **Calculate the Mean:**
The mean is already given as 8.

2. **Find the Deviations from the Mean:**
Calculate the absolute deviation of each data point from the mean.

The data points are: 5, 5, 5, 6, 9, 10, 10, 10, 10, and 10.

Now, calculate the absolute deviation for each value:
- \( |5 - 8| = 3 \)
- \( |5 - 8| = 3 \)
- \( |5 - 8| = 3 \)
- \( |6 - 8| = 2 \)
- \( |9 - 8| = 1 \)
- \( |10 - 8| = 2 \)
- \( |10 - 8| = 2 \)
- \( |10 - 8| = 2 \)
- \( |10 - 8| = 2 \)
- \( |10 - 8| = 2 \)

Thus, the deviations are:
\[ 3, 3, 3, 2, 1, 2, 2, 2, 2, 2 \]

3. **Calculate the Mean of the Absolute Deviations:**
Now, we need to find the mean of these absolute deviations.

First, sum the absolute deviations:
\[
3 + 3 + 3 + 2 + 1 + 2 + 2 + 2 + 2 + 2 = 3 \times 3 + 2 \times 6 + 1 = 9 + 12 + 1 = 22
\]

Now, divide this sum by the number of data points (10):
\[
\text{Mean Absolute Deviation} = \frac{22}{10} = 2.2
\]

Therefore, the mean absolute deviation (MAD) is \( \boxed{2.2} \).