The first four deviations from the mean in a sample of n= 5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.

Answer : Step 1 : Given the first four deviations from the mean in a sample of n= 5 reaction times were 0.3, 0.9, 1.0, and 1.3. We know that reaction times were 0.3, 0.9, 1.0, and 1.3. 0.3+0.9+1.0+1.3 =0 Therefore the total of four deviations is 3.5 The sum of the deviations of items taken from Actual Mean is always be equal to 0 irrespective of the number of items. So the fifth deviation must be equal to 0. Then the fifth deviation must be equal to 0-3.5 = -3.5 OR 0.3+0.9+1.0+1.3+x =0 = 3.5 + x = 0 = x = -3.5 Now we have to find the five deviation from the mean. X items : 8.3 8.9 9.0 9.3 and 4.5 Sum 8.3+8.9+9.0+9.3+4.5 = 40 Then the number of items is 5 Then the formula of the mean is Sum of the items Mean = No. of items 40 Mean = 5 Mean = 8 Here the first four deviation are .3 .9 1.0 1.3 Now we have to find the five deviation is The fifth deviation is Deviation = Item-Mean Deviation = 8.0 - 3.5 Deviation = -3.5 Therefore the fifth deviation from the mean is 3.5