Question

What is the sum of the
absolute deviations in the
following dataset: 63, 25, 74,
52, 63, 12, 46? The mean of
the dataset is 47.9. Express
your answer as a decimal
rounded to the nearest tenth.

Answer 1

To calculate the sum of the absolute deviations of the dataset from the mean, we first use the given mean of 47.9 and then find the absolute deviation of each data point from the mean.

The dataset is: 63, 25, 74, 52, 63, 12, 46.
The mean is: 47.9.

Now, we compute the absolute deviations:

1. For 63:
\(|63 - 47.9| = |15.1| = 15.1\)

2. For 25:
\(|25 - 47.9| = |-22.9| = 22.9\)

3. For 74:
\(|74 - 47.9| = |26.1| = 26.1\)

4. For 52:
\(|52 - 47.9| = |4.1| = 4.1\)

5. For 63 (again):
\(|63 - 47.9| = |15.1| = 15.1\)

6. For 12:
\(|12 - 47.9| = |-35.9| = 35.9\)

7. For 46:
\(|46 - 47.9| = |-1.9| = 1.9\)

Now we sum all the absolute deviations:

\[
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9
\]

Calculating this step by step:

- \(15.1 + 22.9 = 38.0\)
- \(38.0 + 26.1 = 64.1\)
- \(64.1 + 4.1 = 68.2\)
- \(68.2 + 15.1 = 83.3\)
- \(83.3 + 35.9 = 119.2\)
- \(119.2 + 1.9 = 121.1\)

The sum of the absolute deviations is \(121.1\).

Thus, the final answer is:

\[
\boxed{121.1}
\]