Key elements • Mean (average)

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Statistics 

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Key elements 
• Mean (average) 
• Median 
• Mode 
• Standard deviation 

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Mean 
• Mean = Sum of the entities/number of the entities 
• % Change in Average = % Change in sum 
• 1,2,3 – mean = 2 
• 1,2,2,3 – mean = 2 

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Standard Deviation 
Step 1: Compute mean for the given set of numbers. 
Step 2: Compute Deviation of each term from the mean. Deviation is computed by subtracting 
mean from each term. You will have as many deviations as the number of terms in the set.
Step 3: Square the deviations
Step 4: Compute the average of the squared deviations. This is the penultimate step. The result 
of this step is called Variance.
Step 5: Square root of Variance is the standard deviation.
Set {1,4,5,6,9} 
Mean = (1+4+5+6+9)/5 = 5 
Deviations from mean = {-4, -1, 0, 1, 4} 
Square the deviations = {16, 1, 0, 1, 16} 
Average of the deviations = (16+1+0+1+16)/5 = 6.8 
Variance = 6.8 
SD = 

6.8 = 2.6 

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SD 

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Adding a new element to the set 

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If a constant 'k' is added or subtracted from each term in a set, the standard 
deviation does not change.
• Because, the relative difference between the numbers (and in turn the 
deviation from the mean) remain unchanged. 
• Add 2 
• Set {1,4,5,6,9} 
• Mean = (1+4+5+6+9)/5 = 5 
• Deviations from mean = {-4, -1, 0, 1, 4} 
• New Set {3,6,7,8,11} 
• New Mean = (3+6+7+8+11)/5 = 7 
• New Deviations from mean = {-4, -1, 0, 1, 4} – same 
• The rest is same 

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