Question

What is the sum of the
absolute deviations in the
following dataset: 68, 51, 75,
78, 94, 35? The mean is 66.8.

15.9
59
401
95.4

Answer 1

To find the sum of the absolute deviations from the mean in the dataset \(68, 51, 75, 78, 94, 35\) with a mean of \(66.8\), we follow these steps:

1. Calculate the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value.
2. Sum these absolute deviations.

Here are the steps:

1. Calculate the absolute deviations:

\[
|68 - 66.8| = |1.2| = 1.2
\]
\[
|51 - 66.8| = |-15.8| = 15.8
\]
\[
|75 - 66.8| = |8.2| = 8.2
\]
\[
|78 - 66.8| = |11.2| = 11.2
\]
\[
|94 - 66.8| = |27.2| = 27.2
\]
\[
|35 - 66.8| = |-31.8| = 31.8
\]

2. Now sum these absolute deviations:

\[
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8
\]

Calculating this step-by-step:

\[
1.2 + 15.8 = 17
\]
\[
17 + 8.2 = 25.2
\]
\[
25.2 + 11.2 = 36.4
\]
\[
36.4 + 27.2 = 63.6
\]
\[
63.6 + 31.8 = 95.4
\]

Therefore, the sum of the absolute deviations is \( \boxed{95.4} \).