# 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.