Question

Mean absolute deviation of 9,13,43,55

Answer 1

To find the Mean Absolute Deviation (MAD) for the data set \(9, 13, 43, 55\), follow these steps:

1. **Calculate the Mean** of the data set.
2. **Calculate the absolute deviations** from the mean.
3. **Find the mean of those absolute deviations**.

### Step 1: Calculate the Mean

\[
\text{Mean} = \frac{9 + 13 + 43 + 55}{4} = \frac{120}{4} = 30
\]

### Step 2: Calculate the Absolute Deviations

Now we calculate the absolute deviations from the mean:

- For \(9\): \(|9 - 30| = 21\)
- For \(13\): \(|13 - 30| = 17\)
- For \(43\): \(|43 - 30| = 13\)
- For \(55\): \(|55 - 30| = 25\)

### Step 3: Calculate the Mean of Absolute Deviations

\[
\text{Mean Absolute Deviation} = \frac{21 + 17 + 13 + 25}{4} = \frac{76}{4} = 19
\]

Thus, the Mean Absolute Deviation (MAD) of the data set \(9, 13, 43, 55\) is **19**.