Questions: A group of data items and their mean are given. 198,225,255,258,270,342; Mean = 258 a. Find the deviation from the mean for each of the data items. b. Find the sum of the deviations in part (a). a. Type the deviation from the mean for each of the data items. 198 225 255 258 270 342 (Simplify your answers.)

Solution Steps

Given the data items \(198, 225, 255, 258, 270, 342\) and the mean \( \mu = 258 \), we calculate the deviation from the mean for each data item using the formula:

\[ \text{Deviation} = x - \mu \]

Calculating the deviations:

• For \(198\): \(198 - 258 = -60\)
• For \(225\): \(225 - 258 = -33\)
• For \(255\): \(255 - 258 = -3\)
• For \(258\): \(258 - 258 = 0\)
• For \(270\): \(270 - 258 = 12\)
• For \(342\): \(342 - 258 = 84\)

Thus, the deviations from the mean are:

\[ \text{Deviations} = [-60, -33, -3, 0, 12, 84] \]

Next, we find the sum of the deviations calculated in Step 1:

\[ \text{Sum of Deviations} = -60 + (-33) + (-3) + 0 + 12 + 84 \]

Calculating this gives:

\[ \text{Sum of Deviations} = 0 \]

Final Answer