CALCULATING THE STANDARD DEVIATIONS FOR DATA SET 1 AND DATA 2
Data Set 1: (Math) Chapter 5 Review Test
(Calculating Mean, Variance, Standard Deviation)
Test Scores Step 1: Step 2:
X Difference (X-M) Square (X-M)2
100 – 85.2 14.8 (14.8)2 = (14.8 x 14.8) = 219.04
98 12.8 163.84
96 10.8 116.64
92 6.8 46.24
87 1.8 3.24
82 – 3.2 10.24
76
75
75
71
N = (Number of Test Score (X)) = X=10
Sum = (Total of X) = 852
MEAN (Average) = (Sum divided by N) = 852 /10 = (M) = 85.2
Step 1 = (Difference between each Score and Mean (X – M); example (100 – 85.2) = 14.80
Step 2 = (Square the Difference b/w each Score and Mean (X -M)2; example (100-85.2) = (14.8)2 = 219.04 Step 3: Sum of Squares: (Total of (X-M)2 example = 219.04 + 163.84 + – – = (Total of Sum of squares)
Step 4: Divide Total of sum of squares by N to obtain the Variance = (Total of Sum of Squares) / N = (?)
Step 5: Standard deviation = square root of Step 4. = √ Variance
STANDARD DEVIATION =
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Completing the above Data Set 1 and deriving the standard deviation will help you solve the Data Sets problems.