Questions: Question 7, 12.3.13 Part 1 of 3 Find a. the mean; b. the deviation from the mean for each data item; and c. the sum of the deviations in part (b) for the following group of data items. 138,141,147,151,153 a. The mean is .

Question 7, 12.3.13 Part 1 of 3 Find a. the mean; b. the deviation from the mean for each data item; and c. the sum of the deviations in part (b) for the following group of data items. 138,141,147,151,153 a. The mean is .
Transcript text: Question 7, 12.3.13 Part 1 of 3 Find $\mathbf{a}$. the mean; $\mathbf{b}$. the deviation from the mean for each data item; and $\mathbf{c}$. the sum of the deviations in part (b) for the following group of data items. \[ 138,141,147,151,153 \] a. The mean is $\square$ .
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Solution

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Solution Steps

To solve this problem, we need to follow these steps:

  1. Calculate the Mean: Add all the data items together and divide by the number of items to find the mean.
  2. Calculate Deviations from the Mean: Subtract the mean from each data item to find the deviation for each item.
  3. Sum of Deviations: Add all the deviations calculated in the previous step.
Step 1: Calculate the Mean

To find the mean of the data set \([138, 141, 147, 151, 153]\), we sum all the data items and divide by the number of items:

\[ \text{Mean} = \frac{138 + 141 + 147 + 151 + 153}{5} = \frac{730}{5} = 146 \]

Step 2: Calculate Deviations from the Mean

For each data item, subtract the mean to find the deviation:

  • For 138: \(138 - 146 = -8\)
  • For 141: \(141 - 146 = -5\)
  • For 147: \(147 - 146 = 1\)
  • For 151: \(151 - 146 = 5\)
  • For 153: \(153 - 146 = 7\)

Thus, the deviations are \([-8, -5, 1, 5, 7]\).

Step 3: Sum of Deviations

Add all the deviations calculated in the previous step:

\[ -8 + (-5) + 1 + 5 + 7 = 0 \]

Final Answer

  • The mean is \(\boxed{146}\).
  • The deviations from the mean are \([-8, -5, 1, 5, 7]\).
  • The sum of the deviations is \(\boxed{0}\).
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