Find 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. \( 28,78,53,28,103 \) a. The mean is (Simplify your answer.)

We are given the data items: 28, 78, 53, 28, 103. Step 1. Calculate the mean:  Add all the items and divide by the number of items.  Mean = (28 + 78 + 53 + 28 + 103) / 5 = 290 / 5 = 58 Step 2. Determine the deviation from the mean for each data item:  For 28: Deviation = 28 − 58 = –30  For 78: Deviation = 78 − 58 = 20  For 53: Deviation = 53 − 58 = –5  For 28: Deviation = 28 − 58 = –30  For 103: Deviation = 103 − 58 = 45 Step 3. Sum the deviations:  Sum = (–30) + 20 + (–5) + (–30) + 45 = 0 Answers: a. The mean is 58. b. The deviations are –30, 20, –5, –30, and 45, respectively. c. The sum of the deviations is 0.